Question

Nichols Inc. is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's IRR can be less than the cost of capital or negative, in both cases it will be rejected.

Year	0	1	2	3	4	5
Cash flows	−$1,250	$325	$325	$325	$325	$325

a. 10.92%

b. 9.43%

c. 11.47%

d. 10.40%

e. 9.91%

Westwood Painting Co. is considering a project that has the following cash flow and cost of capital (r) data. What is the project's MIRR? Note that a project's MIRR can be less than the cost of capital (and even negative), in which case it will be rejected.

r.	12.25%
Year	0	1	2	3	4
Cash flows	−$850	$300	$320	$340	$360

a. 18.22%

b. 16.56%

c. 13.42%

d. 20.04%

e. 14.91%

Worthington Inc. is considering a project that has the following cash flow data. What is the project's payback?

Year	0	1	2	3
Cash flows	−$500	$150	$200	$300

a. 2.25 years

b. 3.03 years

c. 2.03 years

d. 2.50 years

e. 2.75 years

Craig's Car Wash Inc. is considering a project that has the following cash flow and cost of capital (r) data. What is the project's discounted payback?

r.	10.00%
Year	0	1	2	3
Cash flows	−$900	$500	$500	$500

a. 2.09 years

b. 2.52 years

c. 2.78 years

d. 2.29 years

e. 1.88 years

Answer 1

1)

IRR is the rate of return that makes initial investment equal to present value of cash inflows

Initial investment = Annuity * [1 - 1 / (1 + r)ⁿ] /r

1250 = 325 * [1 - 1 / (1 + r)⁵] /r

Using trial and error method, i.e., after trying various values for R, lets try R as 9.43%

1250 = 325 * [1 - 1 / (1 + 0.0943)⁵] /0.0943

1250 = 325 * 3.846639

1250 = 1,250

Therefore, IRR is 9.43%

2)

Future value of year 1 cash flow = 300 (1 + 0.1225)³ = 424.307105

Future value of year 2 cash flow = 320 (1 + 0.1225)² = 403.202

Future value of year 3 cash flow = 340 (1 + 0.1225)¹ = 381.65

Future value of year 4 cash flow = 360 (1 + 0.1225)⁰ = 360

424.307105 + 403.202 + 381.65 + 360 = 1,569.1591

MIRR = (FV / initial investment)^1/n - 1

MIRR = (1,569.1591 / 850)^1/4 - 1

MIRR = 1.1656 - 1

MIRR = 0.1656 or 16.56%

3)

Cumulative cash flow for year 0 = -500

Cumulative cash flow for year 1 = -500 + 150 = -350

Cumulative cash flow for year 2 = -350 + 200 = -150

Cumulative cash flow for year 3 = -150 + 300 = 150

150 / 300 = 0.5

Project's payback = 2 + 0.5 = 2.50 years

4)

Present value of year 1 cash flow = 500 / (1 + 0.1)¹ = 454.5455

Present value of year 2 cash flow = 500 / (1 + 0.1)² = 413.22314

Present value of year 3 cash flow = 500 / (1 + 0.1)³ = 375.6574

Cumulative cash flow for year 0 = -900

Cumulative cash flow for year 1 = -900 + 454.5455 = -445.4545

Cumulative cash flow for year 2 = -445.4545 + 413.22314 = -32.23136

Cumulative cash flow for year 3 = -32.23136 + 375.6574 = 343.43

32.23136 / 375.6574 = 0.09

Discounted payback = 2 + 0.09 = 2.09 years