Question

A firm with a 14% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows: 0 1 2 3 4 5 Project M -$18,000 $6,000 $6,000 $6,000 $6,000 $6,000 Project N -$54,000 $16,800 $16,800 $16,800 $16,800 $16,800 Calculate NPV for each project. Do not round intermediate calculations. Round your answers to the nearest cent. Project M: $ Project N: $ Calculate IRR for each project. Do not round intermediate calculations. Round your answers to two decimal places. Project M: % Project N: % Calculate MIRR for each project. Do not round intermediate calculations. Round your answers to two decimal places. Project M: % Project N: % Calculate payback for each project. Do not round intermediate calculations. Round your answers to two decimal places. Project M: years Project N: years Calculate discounted payback for each project. Do not round intermediate calculations. Round your answers to two decimal places. Project M: years Project N: years Assuming the projects are independent, which one(s) would you recommend? If the projects are mutually exclusive, which would you recommend? Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?

Answer 1

a). NPV

Calculating NPV of the project, with WACC= 14% will be

Project M: -18000+6000/1.14+6000/1.14^2+6000/1.14^3+6000/1.14^4+6000/1.14^5= 2598.49

Project N: -54000+16800/1.14+16800/1.14^2+16800/1.14^3+16800/1.14^4+16800/1.14^5= 3675.76

b). IRR

For Project M, let r be the IRR, where -18000+6000/1+r+6000/(1+r)^2+6000/(1+r)^3+6000/(1+r)^4+6000/(1+r)^5=0. On solving r is 19.86%

For Project N, let r be IRR, where

-54000+16800/(1+r)+16800/(1+r)^2+16800/(1+r)^3+16800/(1+r)^4+16800/(1+r)^5=0. On solving r is 16.79%

c). MIRR

For project M, MIRR will be (Future value of Positive cashflows at cost of capital/Present value of Intial investment at financing cost)^1/n)-1. Future value of positive cashflows will be 6000*(1.14)^4+6000*(1.14)^3+6000*(1.14)^2+6000*(1.14)+6000= 39660.62. So, MIRR= ((39660.62/18000)^(1/5))-1 =17.12%

Similarly for project N,

MIRR= (((16800*(1.14)^4+16800*(1.14)^3+16800*(1.14)^2+16800*1.14+16800)/54000))^(1/5))-1= 15.51%

d).

For project M, payback period will be 3 years as first rhree years cashflows of 6000 each will be equal to Initial Investment.

For project N, First three years cashflows will be 16800*3= 50400. So, a remaining of 54000-50400= 3600 and it is 21.43% of fourth year cashflow of 16800. So, payback period is 3.21 Years

e).

For project M, discounted cashflows for T1= 6000/1.14= 5263.16, T2= 6000/1.14^2= 4616.81, T3= 4049.83, T4= 3552.48, T5= 3116.21. After four years, cumulative discounted cashflows will be 17481.98. Remaining amount of (18000-17481.98) for investment is 16.62% of the discounted cashflow for 5th year. So, discounted payback period is 4.16 Years.

For project N, discounted cashback for T1= 14736.84, T2= 12927.05, T3= 11339.52, T4= 9946.95, T5= 8725.39. Remaining amount of (54000-48950.36) for investment is 57.87% of the discounted cashflow of 5th year. So, discounted payback period is 4.57 Years.

If the projects are Independent, we can choose to take up both Project M and Project N, as both NPVs are greater than 0.

If the projects are mutually exclusive, then atmost one project needs to be taken up. Then we need to choose Project N, as its NPV is greater than other project.

There is a conflict between NPV and IRR. Considering NPV, Project N is better where as IRR of project M is greater than Project N. This is because of the unrealistic assumption of IRR which is that the cashflows can be reinvested at the same IRR, which is not possible in real world scenario. They can be reinvested for the firm's cost of capital in most of the cases. Because of this drawback, there is a conflict in NPV and IRR.