Your division is considering two investment projects, each of which requires an up-front expenditure of $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions ofdollars):Year Project A Project B1 5202 10 103 15 84 20 6a. What is the regular payback period for each of the projects?b. What is the discounted payback period for each of the projects?c. If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake?d. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?e. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?f. What is the crossover rate?g. If the cost of capital is 10%, what is the modified IRR (MIRR) of each project?

The answer is attached in form of text file below giving solution to each of the question parts in detail.

a. What is the regular payback period for each of the projects?

b. What is the discounted payback period for each of the projects?

c. If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake?

d. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?

e. If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?

f. What is the crossover rate?

g. If the cost of capital is 10%, what is the modified IRR (MIRR) of each project?

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%

answer; competency based pay;