Question

Problem 10-21
Payback, NPV, and MIRR

Your division is considering two investment projects, each of which requires an up-front expenditure of $27 million. You estimate that the cost of capital is 8% and that the investments will produce the following after-tax cash flows (in millions of dollars):

Year	Project A	Project B
1	5	20
2	10	10
3	15	8
4	20	6

1. What is the regular payback period for each of the projects? Round your answers to two decimal places.
   
   Project A years
   
   Project B years
2. 
   
3. 
   
4. 
   
5. What is the discounted payback period for each of the projects? Round your answers to two decimal places.
   
   Project A years
   
   Project B years
6. 
   
7. 
   
8. 
   
9. If the two projects are independent and the cost of capital is 8%, which project or projects should the firm undertake?
   -Select-Project AProject BBoth projects
10. 
    
11. 
    
12. 
    
13. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
    -Select-Project AProject B
14. 
    
15. 
    
16. 
    
17. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?
    -Select-Project AProject B
18. 
    
19. 
    
20. 
    
21. What is the crossover rate? Round your answer to two decimal places.
    %
22. 
    
23. 
    
24. 
    
25. If the cost of capital is 8%, what is the modified IRR (MIRR) of each project? Round your answers to two decimal places.
    
    Project A %
    
    Project B %

Answer 1

Ans(a)

Year Project A cash flow($) Commulated cash flow of project A($) Project B cash flow($) Commulated cash flow of project B($)

0 -25,000,000 -25,000,000 -25,000,000 -25,000,000

1 5,000,000 -20,000,000 20,000,000 -5,000,000

2 10,000,000 -10,000,000 10,000,000 5,000,000

3 15,000,000 5,000,000 8,000,000 13,000,000

4 20,000,000 25,000,000 6,000,000 19,000,000

For project A , comulated cash flow became positive in between 2nd & 3rd year. Same as for Project B it is in between 1st & 2nd year. So payback period for -

Project A= 2year+10000000/15000000=2.67years

Project B= 1year+5000000/10000000=1.5years

Ans(b)

Year Project A cash flow($) Discounted cash flow @8%(A) Commulated discounted cash flow of project A($) Project B cash flow($) Discounted cash flow @8%(B) Commulated discounted cash flow of project B($)

0 -25,000,000 -25,000,000 -25,000,000 -25,000,000 -25,000,000 -25,000,000

1 5,000,000 4,629,630 -20,370,370 20,000,000 18,518,519 -6,481,481

2 10,000,000 8,573,388 -11,796,982 10,000,000 8,573,388 2,091,907

3 15,000,000 10,208,748 -1,588,234 8,000,000 5,444,666 7,536,573

4 20,000,000 12,603,392 11,015,158 6,000,000 3,781,018 11,317,591

We found that in project A the discounted cumulated Cash flow became positive between year 3 and year 4

Payback period = 3 Years + $ 1,588,234 /$ 12603392 = 3.13 years

We found that in projectB the discounted cumulated Cash flow became positive between year 1 and year 2

Payback period = 1 Year + $6,481,481/$8,573,388 = 1.76 years

Ans(c)

If the two projects are independent and the cost of capital is 8%, which project or projects should the firm undertake?

From the cumulated cash flow table we came to know:

NPV(A) = $ 12,603,392

NPV(B) = $ 11,317,591

As NPV(A) and NPV(B) both are positive both the projects should be selected.

Ans(d)

We calculate NPV using costof capital @5% for both the project

Project A

=−$25,000,000+$5,000,000/1.05+$10,000,000/1.052+$15,000,000/1.053+$20,000,000/1.054

=$18,243,813

Project B

=−$25,000,000+$20,000,000/1.05+$10,000,000/1.052+$8,000,000/1.053+$6,000,000/1.054

=$14,964,829

As NPV(A) > NPV(B) so project A to be selected.

Ans(e)

We calculate NPV using cost of capital @15% for both the project

Project A

=−$25,000,000+$5,000,000/1.15+$10,000,000/1.152+$15,000,000/1.153+$20,000,000/1.154

=$8,207,071

Project B

=−$25,000,000+$20,000,000/1.15+$10,000,000/1.152+$8,000,000/1.153+$6,000,000/1.154

=$8,643,390

As NPV(A) < NPV(B) so project B to be selected.

Ans(f)

Crossover rate is the discount rate where NPV of both the projects are equal.

We calculate the crossover rate as the IRR of the differential cash flow

Year Project A Cash Flow Project B Cash Flow A-B

0 -$ 2,50,00,000 -$ 2,50,00,000 $ 0

1 $ 5,000,000 $ 20,000,000 -$ 1,50,00,000

2 $ 10,000,000 $ 10,000,000 $ 0

3 $ 15,000,000 $ 8,000,000 $ 7,000,000

4 $ 20,000,000 $ 6,000,000 $ 14,000,000

We found the IRR as:

NPV=−$1,50,00,000/(1+IRR)+$7,000,000/(1+IRR)3+$14,000,000/(1+IRR)4..........................(1)

Solving the equation (1)we get,

IRR = 13.53%

Ans(g)

Year Project A Cash Flow PV of cash outflow FV of cash inflow@10% MIRR= (FV of cash inflow/PV of cash outflow)^(1/Years of life) -1

0 -$ 25,000,000 $ 25,000,000 21.93%

1 $ 5,000,000 $ 6,655,000

2 $ 10,000,000 $ 12,100,000

3 $ 15,000,000 $ 16,500,000

4 $ 20,000,000 $ 20,000,000

Total $ 25,000,000 $ 55,255,000