Answer:
a. What is the regular payback period for each of the projects?
- project A: 2.67 years
- project B: 1.5 years
b. What is the discounted payback period for each of the projects?
- project A: 3.07 years
- project B: 1.83 years
c. If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake?
- project A: NPV = $12.74 million
- project B: NPV = $11.55 million
- both projects have positive NPVs so they should both be chosen
d. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
- project A: NPV = $18.24 million (higher NPV, so this project should be selected)
- project B: NPV = $14.96 million
e. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?
- project A: NPV = $8.21 million
- project B: NPV = $8.64 million (higher NPV, so this project should be selected)
f. What is the crossover rate?
g. If the cost of capital is 10%, what is the modified IRR (MIRR) of each project?
- MIRR project A = 21.93%
- MIRR project B = 20.96%
Explanation:
Project A Project B
investment required -$25,000,000 -$25,000,000
cash flow 1 $5,000,000 $20,000,000
cash flow 2 $10,000,000 $10,000,000
cash flow 3 $15,000,000 $8,000,000
cash flow 4 $20,000,000 $6,000,000
a. What is the regular payback period for each of the projects?
project A: 2 years ($15 million) + 10/15 = 2.67 years
project B: 1 year ($20 million) + 5/10 = 1.5 years
b. What is the discounted payback period for each of the projects?
interest rate = 10%
discounted cash flows Project A Project B
5/1.1 = 4.55 20/1.1 = 18.18
10/1.1² = 8.26 10/1.1² = 8.26
15/1.1³ = 11.27 8/1.1³ = 6.01
20/1.1⁴ = 13.66 6/1.1⁴ = 4.1
project A: 3 years ($24.08 million) + 0.92/13.66 = 3.07 years
project B: 1 year ($18.18 million) + 6.82/8.26 = 1.83 years
c. If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake? using excel spread sheet an NPV function:
project A: NPV = $12.74 million
project B: NPV = $11.55 million
both projects have positive NPVs so they should both be chosen
d. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
project A: NPV = $18.24 million (higher NPV, so this project should be selected)
project B: NPV = $14.96 million
e. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?
project A: NPV = $8.21 million
project B: NPV = $8.64 million (higher NPV, so this project should be selected)
f. What is the crossover rate?
investment project A - investment project B = 0
cash flow 1 project A - cash flow 1 project B = 5 - 20 = -15
cash flow 2 project A - cash flow 2 project B = 10 - 10 = 0
cash flow 3 project A - cash flow 3 project B = 15 - 8 = 7
cash flow 4 project A - cash flow 4 project B = 20 - 6 = 14
now using excel spreadsheet we determine IRR: 13.53%
g. If the cost of capital is 10%, what is the modified IRR (MIRR) of each project?
MIRR = {ⁿ√ [FV(positive cash flows x cost of capital)] / [PV(initial outlays)]} - 1
future value of positive cash flows project A = (5 x 1.1³) + (10 x 1.1²) + (15 x 1.1) + 20 = 6.655 + 12.1 + 16.5 + 20 = 55.255
future value of positive cash flows project A = (20 x 1.1³) + (10 x 1.1²) + (8 x 1.1) + 6 = 26.62 + 12.1 + 8.8 + 6 = 53.52
PV initial outlays for both projects = -$25,000
n = 4
MIRR project A = {⁴√ [55.255 / -25]} - 1 = 1.2193 - 1 = 0.2193 or 21.93%
MIRR project B = {⁴√ [53.52 / -25]} - 1 = 1.2096 - 1 = 0.2096 or 20.96%
