Question

A project costs $45,000 today, and will produce a single, one-time after tax cash flow of $330,000 in the future. What is the IRR of this project under each of the following scenarios? a. The future cash flow occurs in 5 years. b. The future cash flow occurs in 10 years. c. The future cash flow occurs in 15 years. d. The future cash flow occurs in 20 year

Answer 1

a) 48.95%

b) 22.05%

c) 14.21%

d) 10.48%

Step-by-step explanation:

Data provided in the question:

Cost of project today i.e present value = $45,000

Future value = $330,000

Now,

IRR =
`[\frac{\text{Future value}}{\text{initial cost}}]^{(1)/(n)` - 1

Here,

n = Number of years for which cash flow occurs

thus,

a) The future cash flow occurs in 5 years

n = 5

IRR =
`[(\$330,000)/(\$45,000)]^{(1)/(5)` - 1

= 0.4895

or

= 48.95%

b) The future cash flow occurs in 10 years

n = 10

IRR =
`[(\$330,000)/(\$45,000)]^{(1)/(10)` - 1

= 0.2205

or

= 22.05%

c) The future cash flow occurs in 10 years

n = 15

IRR =
`[(\$330,000)/(\$45,000)]^{(1)/(15)` - 1

= 0.1421

or

= 14.21%

d) The future cash flow occurs in 10 years

n = 15

IRR =
`[(\$330,000)/(\$45,000)]^{(1)/(20)` - 1

= 0.1048

or

= 10.48%