A prospective MBA student earns $45,000 per year in her current job and expects that amount to increase by 8% per year. She is considering leaving her job to attend business school for two years at a cost of $30,000 per year. She has been told that her starting salary after business school is likely to be $95,000 and that amount will increase by 14% per year. Consider a time horizon of 10 years, use a discount rate of 14%, and ignore all considerations not explicitly mentioned here. 

 

Assume all cash flows occur at the start of each year (i.e., immediate, one year from now, two years from now,..., nine years from now). Also assume that the choice can be implemented immediately so that for the MBA alternative the current year is the first year of business school. 

 

What is the net present value of the more attractive choice? 

 

Answer:

Most attractive choice is option 2 because net present value is higher in option 2 in comparison to option 1.

Net present value in option 2 = 462977

Step-by-step explanation

Option 1: Continue with current job at $45000 for 10 years at 6% increment

Calculating the present value for 10 years:

Year 1 = 45000*1/(1+0.14)^1 = 45000/1.14 = 45000*1/1.14= 45000*0.877 = 39465

Year 2 = 45000*1.08*1/(1+0.14)^2 =48600*0.769 = 37373.4

Year 3 = 48600*1.08*1/(1+0.14)^3 = 52488*0.675 =35429.4

Year 4 = 52488*1.08*1/(1+0.14)^4 = 56687.04*0.592=33558.73

Year 5 = 56687.04*1.08*1/(1+0.14)^5 = 61222*0.519=31774.22

Year 6 = 61222*1.08*1/(1+0.14)^6 =66119.76*0.455=30084.49

Year 7 =66119.76*1.08*1/(1+0.14)^7 =71409.34*0.399=28492.33

Year 8 =71409.34*1.08*1/(1+0.14)^8 =77122.09*0.350=26992.73

Year 9 = 77122.09*1.08*1/(1+0.14)^9 =83291.85*0.307=25570.60

Year 10 = 83291.85*1.08*1/(1+0.14)^10 =89955.20*0.270=24287.90

Total of present value to be received in 10 years if continuing present job = 313028.8 i.e. 313029

Option 2: Leaving current job for 2 years and then take new job at $95000 for 8 years

a) Calculating the present value of cost of studying for 2 years:

Year 1 = 30000*1/(1+0.14)^1 = 30000/1.14 = 30000*0.877 = 26310

Year 2 = 30000*1/(1+0.14)^2 = 30000/(1.14)^2 = 30000*0.769 = 23070

Total present value of cost of studying = 49380

b) Calculating the present value of $95000 for 8 years at 14% increment

Year 3 = 95000*1/(1+0.14)^3 = 95000*0.675 = 64125

Year 4 = 95000*1.14*1/(1+0.14)^4 =108300 *0.592 = 64113.6

Year 5 = 108300*1.14*1/(1+0.14)^5 =123462 *0.519 =64076.78

Year 6 = 123462*1.14*1/(1+0.14)^6 =140746.68*0.455=64039.74

Year 7 =140746.68*1.14*1/(1+0.14)^7 =160451.21*0.399=64020.03

Year 8 =160451.21*1.14*1/(1+0.14)^8 =182914.38*0.350=64020.03

Year 9 = 182914.38*1.14*1/(1+0.14)^9 =208522.39*0.307=64016.37

Year 10 = 208522.39*1.14*1/(1+0.14)^10 =237715.52*0.269=63945.47

Total present value of salary received after studying =512357.02

Net present value in option 2 = Total present value of salary received after studying - Total present value of cost of studying

= 512357.02 - 49380 = 462977.02 i.e. 462977

Most attractive choice is option 2 because net present value is higher in option 2 in comparison to option 1.

Net present value in option 2 = 462977