8 Capital Budgeting and Costs of Capital Don’t tell me what you value, show me your budget, and I’ll tell you what you value

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 8 Capital Budgeting and Costs of Capital Don’t tell me what you value, show me your budget, and I’ll tell you what you value. Joe Biden In Chapter 7, we discussed pro forma financial statements. One of the important inputs is planned long-term investments. How do we decide what long-term investments should be made? In this chapter, we provide tools that enable entrepreneurs to answer this question, which is called the “capital budgeting decision.” The amount of estimated long-term investments is referred to as the capital budget. These decisions are called capital budgeting decisions because they involve committing significant funds for a long horizon. These investments range from acquiring fixed equipment and buildings to launching new products and entering new markets. Because these decisions impact a company’s business strategies and operations for years to come, they warrant detailed analysis. The tools we describe in this chapter are commonly used in practice. Each of these tools performs some form of cost-benefit analysis. The costs include direct operating costs, overhead, and costs of the allocated capital. It is important to consider the costs of capital because accounting profits do not take into account returns to investors. For a business to be successful in the long term, it must earn adequate returns for investors. The first section of this chapter covers the basic concepts of time value of money; the second section covers the calculation of costs of capital; and the third section covers capital budgeting methods. Time Value of Money An investment is worth undertaking if it creates additional value to the investor. For example, you have the opportunity to buy a house in a foreclosure for $80,000 and you estimate that it will cost $20,000 to fix it up to be marketable. You think you can sell the house for $115,000 when the remodeling is complete. Is this a valuable investment? At first glance, the purchase price EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. 258  Measuring Performance in the Long Term plus remodeling puts the total costs at $100,000 ($80,000 + $20,000). If you are able to get $115,000, you will have a $15,000 ($115,000 − $100,000) profit or a profit margin of 15 percent (($15,000/$100,000) × 100 percent). Are we missing any factors in this calculation? Does it matter how long it takes for you to sell the house? Would your conclusion be different if you have to borrow some of the $80,000? What if you know that there will be three other properties going into foreclosure in the same neighborhood soon? Let us consider each of these factors in the context of time value of money. From an accounting perspective, your profit from this investment is $15,000. But what is the value of this investment? The answer depends on your required return on your investment. To illustrate, assume that you can invest in a real estate mutual fund that has a similar risk to the property under consideration. You can earn 10 percent per year on this mutual fund. So if you have $100,000, your earnings in year one will be $10,000 ($100,000 × 0.10), and the ending value of your investment will be $110,000 ($100,000 × 1.10). If you leave this investment for another year, the earnings in the second year will be $11,000 ($110,000 × 0.10), and the ending value after two years will be $121,000 ($110,000 × 1.10). Notice that your earnings in year 2 is $11,000, not $10,000, because it is based on $110,000, not the original investment of $100,000. Another way to look at the earnings in year 2 is that you earn $10,000 on the original investment ($100,000 × 0.10) and $1,000 on the earnings from year 1 ($10,000 × 0.10), totaling $11,000 ($10,000 + $1,000). This concept is called compound interest. Now we can compare the value of the foreclosed property with this mutual fund. If it takes one year to remodel and sell the property, you will earn $15,000 in one year, higher earnings than the $10,000 on the mutual fund. If it takes two years to sell the property, you will earn $15,000 over two years, whereas the mutual fund will generate $21,000 ($10,000 + $11,000) over two years; the mutual fund is a better investment. 8.1 Computing Future Value The process of computing future value is called compounding. The formula for computing future value is: Future value = Present value × (1 + r)t where r is the return per period and t is the number of time periods. For example, a real estate mutual fund provides an estimated return of 10 percent per year. An investor starts with $100,000. The future value of her investment will be: After 1 year, Future value1 = $100,000 (1.10)1 = $110,000 EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Capital Budgeting and Costs of Capital 259 After 2 year, Future value2 = $100,000 (1.10)2 = $121,000 After 3 year, Future value3 = $100,000 (1.10)3 = $133,100 The future value formula takes into account compounding, i.e. the investor’s ability to earn interest on interest. The simple fixer-upper investment illustrates several common themes in project analysis. The startup costs of a project are usually relatively straightforward to estimate. A fair amount of research is needed but the information is usually available. The size and timing of future cash flows, which include estimated revenues and production costs, are harder to predict. Figure 8.1 shows the cash flows of the foreclosure fixer-upper, assuming that it will take you one year to do the remodeling and another year to sell the property. When considering an investment, we need to incorporate its required return when comparing inflows (benefits, revenues) against outflows (costs). A useful approach to summarize inflows, outflows, and required return is to compute the present value of all cash flows. The process of computing present value is called discounting. The interest rate used in the calculation is called the discount rate. When finance professionals refer to the value of an investment, they often mean the present value of its cash flows because that is the most common measure. We will discuss more business valuation methods in Chapter 9. Box 8.2 shows how to compute present value. For the fixer-upper project, the estimated return on the real estate mutual fund (10 percent) is a good proxy for its required return because the fund is a viable alternative investment with similar risks. The present value of the initial purchase costs is $80,000 because the cash flow occurs today. The present value of the remodeling costs is $18,182 ($20,000/1.10). Total cash outflows in present value are $98,182. The present value of the future resale price is $95,041 ($115,000/1.102). Since the present value of its cash inflow is less than Today (t = 0) Year 1 (t = 1) Year 2 (t = 2) −$80,000 −$20,000 +$115,000 Purchase Costs Remodel Costs Resale Figure 8.1 Timeline of Fixer-Upper Cash Flow EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. 260  Measuring Performance in the Long Term 8.2 Computing Present Value The process of computing present value is called discounting. The formula for computing present value is: Present value0 = Future valuet (1 + r)t where r is the return per period and t is the number of time periods. For example, an investor desires to have $2,000,000 at the time of retirement. She finds a mutual fund that provides an estimated return of 8 percent per year. How much does she have to invest today to reach her retirement goal? The amount of the investment today is call the present value and we usually refer to today as t = 0. If the investor plans to retire in 10 years, she needs to invest: Present = value $2, 000, 000 = $926, 387 (1.08)10 If she plans to retire in 20 years, she needs to invest: Present = value $2, 000, 000 = $429, 096 (1.08)20 If she plans to retire in 30 years, she needs to invest: Present = value $2, 000, 000 = $198, 755 (1.08)30 You can verify that the invested amount is sufficient given the estimated return. For example, the future value of $198,755 invested at 8 percent per year for 30 years is $2,000,003 ($198,755 × 1.0830). that of its cash outflows, this is not a valuable investment. Another way to look at this investment is that it takes an initial commitment of $80,000 today. The present value of the resale price net of remodeling cost is $76,859 ($95,041 − $18,182). We reach the same conclusion that this is not a valuable investment because after taking into account the required return of 10 percent, its net present value is less than the initial startup costs. Now let us consider the question of borrowing part of the startup costs. Will the value of this project change if part of the investment is financed by debt? The classic finance textbook answer is, “The value will remain unchanged if we assume that there is no tax and no bankruptcy cost.” Since EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Capital Budgeting and Costs of Capital 261 both taxes and bankruptcy costs exist, the answer depends on how the risk of the business will be affected when debt is used. Chapter 3 introduces different forms of financing and general lending criteria and Chapter 7 discusses factors to consider and frameworks to use when making long-term financing decisions. We will assume that you adopt a conservative approach by borrowing 40 percent of the startup costs and will be able to make debt payments even in the worst-case scenario.1 In other words, the risk of the project will not be greatly affected by the amount of borrowing. To keep this example simple, we assume you will pay interest only in the first year and repay the entire loan plus interest in the second year. The after-tax cost of borrowing is 4.20 percent per year. Recall that the purchase price is $80,000. This means that you will borrow $32,000 ($80,000 × 0.40) today (year 0). Interest on this loan is $1,344 ($32,000 × 0.042) per year. In year 2, you will repay the loan when you sell the property. Figure 8.2 shows the cash flows with borrowing. The accounting profit is reduced by the interest expense and will be $12,312 ($15,000 − $1,344 − $1,344). But what about the present value of these cash flows? The initial cash flow is reduced by the loan amount to $48,000 ($80,000 − $32,000). The present value of year 1’s remodeling and interest costs is $19,404 ($21,344/1.10). For year 2, the present value of the resale price less interest and loan repayment is $67,484 ($81,656/1.102). The present value of the resale price net of all expenses, including interest, is $48,080 ($67,484 − $19,404). Since the initial startup cost is $48,000, the present value of future cash flow is greater, and this indicates a valuable investment. A key assumption in this example is that borrowing conservatively will not increase the risk of equity. If the risk of equity is increased, the required return will also increase. We will explore the relationship with risk of equity and required return further in the section on costs of capital. Year Cash Flow Without Borrowing Debt Principal 0 −$80,000 −$20,000 −$48,000 2 $115,000 −$32,000 $32,000 Debt After-Tax Interest Cash Flow With Borrowing 1 −$1,344 −$1,344 −$21,344 $81,656 Figure 8.2 Timeline of Fixer-Upper Cash Flows with Borrowing EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. 262  Measuring Performance in the Long Term Table 8.1 Cash Flows of Three Different Properties Year 0 1 2 3 Cash flows of Property 1 Cash flows of Property 2 Cash flows of Property 3 −$80,000 −$100,000 −$65,000 −$20,000 −$30,000 −$10,000 $115,000 $145,000 −$10,000 $100,000 Now, consider the case where there may be other properties available. Table 8.1 shows the estimated cash flows of three properties that all have similar risks. If we ignore the time value of money, each of the three properties generates $15,000 in profits. Since all these properties have similar risks, the estimated return on the real estate mutual fund (10 percent) is a good proxy for their required returns. With a 10 percent discount rate, the present value of the resale value less remodeling costs is $76,860 ($115,000/1.102 − $20,000/1.10) for property 1, $92,562 ($145,000/1.102 − $30,000/1.10) for property 2, and $57,776 ($100,000/1.103 − $10,000/1.102 − $10,000/1.10) for property 3. Notice that the value of all three properties is lower than their initial costs, and none of them is a valuable investment. Another approach to analyze these investments is to compute their annualized returns, called the internal rate of return (IRR). You will need a financial calculator or a spreadsheet for this calculation. The next section provides a brief introduction to using spreadsheets to compute future value, present value, and internal rate of return. Using a Spreadsheet to Compute the Time Value of Money We will use the cash flows of the three properties in Table 8.1 to illustrate how to compute the time value of money using a spreadsheet. Microsoft Excel© is a common spreadsheet software package. To perform calculations, create formulas using cell addresses that identify a cell by its column alphabet and row number. For example, the address of the cell in the upper left corner is A1 because it is located on column A, row 1. To its right is cell B1 (column B, row 1), and below it is cell A2 (column A, row 2). Figure 8.3 shows the cash flows entered into a spreadsheet and the formulas for computing the internal rate of return. The cash flows for property 1 are entered in row 2 in the spreadsheet. The −$80,000 initial purchase price is in cell B2, the −$20,000 remodeling cost is in cell C2, and the resale price of $115,000 is in cell D2. For property 1, the sale occurs in year 2, so there is no value entered in year 3, cell E2. To compute the internal rate of return for property 1, enter the formula =IRR(B2:D2) into cell F2. IRR is the spreadsheet function that computes internal rate of return, and the cell reference, B2:D2, directs the spreadsheet to use values between cells B2 and D2, meaning cells B2, C2, and D2, in the calculation. It takes EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Capital Budgeting and Costs of Capital A 1 B Year C D 1 2 -$80,000 - $ 2 0 ,0 0 0 $115,000 -$30,000 $145,000 2 C ash flows of Property 1 3 C ash flows of Property 2 4 $ 100,000 C ash flows of Property 3 -$65,000 -$ 10,000 -$ F E o 10,000 263 3 IRR 8.05% 6.35% $ 100,000 6.30% =IRR(B2:D2) = IR R (B 3 D 3 ) =IRR(B4£4) Figure 8.3 Using a Spreadsheet to Compute the Internal Rate of Return two years to remodel property 3, which is expected to be sold in year 3. Its cash flows are entered in row 4. The formula for computing its internal rate of return is =IRR(B4:E4) and is entered into cell F4. Figure 8.3 shows the results of the calculations. The internal rate of return is 8.05 percent for property 1, 6.35 percent for property 2, and 6.30 percent for property 3. Even though property 1 has the highest internal rate of return at 8.05 percent, it is still below the 10 percent an investor can earn on a real estate mutual fund. Therefore, these properties are inferior investments compared with the mutual fund. A spreadsheet is also a useful tool for computing present values. Figure 8.4 illustrates two methods for calculating the present value of future cash flows for property 1. In the first method, the cash flows are entered in row 16 and the present values are computed in row 17. The present value for the remodeling cost in year 1 is −$18,182 (−$20,000/1.11). It is computed in cell C17 and the formula is =C16/(1+B13)^C15 where C16 contains the remodeling cash flow of −$20,000, B13 contains the required return of 10 percent, and C15 contains the year. The ^ sign tells the spreadsheet to treat the following value as an exponent. The calculation for present value of the resale price is similar. In cell D17, the formula is =D16/(1+B13)^D15, which, when replaced with values, will look like this =$115,000/(1.10)2. The present value of future cash flows is the present value of resale price less the remodeling cost, $76,860 ($95,041 − $18,182). The formula in cell B19 is =C17+D17. Notice that spreadsheet software does not round off decimal places when performing calculations, even if you change the format to display in whole dollars. In the second method, we use spreadsheet function “NPV” to compute the present value of multiple cash flows in one formula. In cell B19, we enter the formula = NPV(B13, C16:D16), which instructs the software to use a discount rate in cell B13 (10 percent) to compute the present values of all cash flows between cells C16 through D16. Notice that the first cell contains the cash flow that occurs in year 1, the remodeling cost, not the initial purchase price. This is an assumption used in most spreadsheet software. If you use cash flow from year 0 as the first cell, the result will be wrong. Of course both methods return the same answer of $76,860. Now you can practice these EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 8/8/2021 1:46 AM via AMERICAN PUBLIC UNIV SYSTEM AN: 1028891 ; Miranda S. Lam, Gina Vega.; Entrepreneurial Finance : Concepts and Cases Account: s7348467 Copyright © 2016. Routledge. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. 264  Measuring Performance in the Long Term a Method 1 Tx A B C D 11 12 13 10 % Required return 14 15 Year 0 1...