Polycorp is considering an investment in new plant of $3.15 million. The project will be partially financed with a loan of $2,000,000 which will be repaid over the next five years in equal annual end of year instalments at a rate of 6.25 percent pa. Assume straight-line depreciation over a five-year life, and no taxes.

The projects cash flows before loan repayments and interest are shown in the table below. Cost of capital is 12.65% pa (the required rate of return on the project). A salvage value of $255,000 is expected at the end of year five and is included in the cash flows for year five below. Ignore taxes and inflation. Year Year One Year Two Year Three Year Four Year Five Cash Inflow 890,000 830,000 815,000 910,000 1045,000

You are required to calculate:

(1) The amount of the annual loan repayment and produce a repayment schedule.

(2) NPV of the project (to the nearest dollar)

(3) IRR of the project (as a percentage to two decimal places)

(4) AE, the annual equivalent for the project (AE or EAV) (to the nearest dollar)

(5) PB, the payback and discounted payback in years (to one decimal place)

(6) ARR, the accounting rate of return (gross and net) (to two decimal places)

(7) PI (present value index or profitability index) (to two decimal places)

(8) Is the project acceptable?

You must provide a decision or explanation for each of the methods in parts (2) to (7). Why or why not (provide a full explanation)? Also a brief explanation of your treatment of Salvage Value and Loan Repayments is required.

 

Answer:

Given in Question:

1. Outlay = 3,150,000 (Investment)

The relevant outlay is the total cost of the project not the amount borrowed or the equity component. (Common errors are to use the amount borrowed 2,000,000 = D or the amount of equity contribution, E = 1,150,000)

2. Cash Flows

Unless otherwise stated these are cash flows before interest and taxes are deducted and do not include salvage value. In this case the questions says that the salvage value is included. Do not deduct repayments or interest as these are financing cash flows and therefore are not relevant.

3. The salvage value at the end of year five is 255,000. The project information says that this is included already in the year five cash flows. A common error is to add it in again.

4. The discount rate for the project is 12.65%. A common error is to use the borrowing rate 6.25%.

5. No taxes and no inflation

 

Ans

(1) Repayment R

R = PV/PVIFA(i = .0625, n = 5)

PV = Amount of the Loan = 2,000,000

PVIFA(i = .0625, n = 5) = 4.1839

= 2000000/4.1839

R = $478026

(Kindly Refer to attached Excel sheet for the schedule)

 

 

(2) NPV of the project

Year Cash Flows

0 -31,50,000

1 8,90,000

2 830000

3 8,15,000

4 9,10,000

5 1045000

NPV = - Outlay +

NPV = -3,150,000 + 890,000/(1.1265)^1 + 830,000/(1.1265)^2 + 815000/(1.1265)^3 + 910,000/(1.1265)^4 + 1045,000/(1.1265)^5

NPV = 5370.75

 

(3) the IRR of the project

At 12.65% the NPV is positive, so the IRR must be higher than 12.65 %.

Using the spreadsheet function we get IRR = 13% You could also get close to this solution manually by interpolation, but given that we have an IRR function in a spreadsheet we can be more accurate and we do not need to approximate. So do not use the interpolation method in quizzes or assignments.

 

4) The Annual Equivalent for the project(AE or EAV)

AE = NPV/PVIFA(i,n)

AE = 5370.75/PVIFA(.1265,5)

PVIFA(.1265,5) = (1-(1+i)-n)/i

AE = 5370.75/4.1839

AE = 1283.67

Common error is to use the debt rate for AE. Use debt rate when doing repayments on debt, use the cost of capital when doing the AE.

 

(5) The Payback in years (to one decimal place)

Year Cash Flow Cumulative

0 -31,50,000 -31,50,000

1 8,90,000 -22,60,000

2 830000 -14,30,000

3 8,15,000 -6,15,000

4 9,10,000 2,95,000

5 1045000 13,40,000

 

Payback Period 4 Years

 

6) ARRG = Average Annual Profit/Initial investment

Profit here is at the EBIT level. In the question we were provided with cash flow forecast.

To calculate ARR we need accounting EBIT forecasts. We must convert the cash flows to profit.

Total Profit = 1,340,000

Average Profit = 268000

ARRG = 268,000/3,150,000 = 8.51%

ARRN = 268,000/[(3150000+255000)/2] = 15.75%

Note that the SV 255,000 is included in year 5 so it needs to be deducted because it is not revenue for accounting purposes.

 

(7) PI (present value index or profitability index)

PVI = PV of cash flows/investment

PV of Cash Flows = NPV + Outlay = 5370.75 + 3,150,000

PVI = 3,155370.75/3,150,000

PVI = 1.0017

 

(8) Is the project acceptable? Why or why not (provide a full explanation)?

NPV is positive

IRR > 12.65% the cost of capital

AE is positive

PVI is greater than 1.

Therefore accept the project adds value according to the objective of maximising value.

PFA