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

Answer:

a) 48.95%

b) 22.05%

c) 14.21%

d) 10.48%

Explanation:

Data provided in the question:

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

Future value = $330,000

Now,

IRR = $[\frac{\text{Future value}}{\text{initial cost}}]^{\frac{1}{n}$ - 1

Here,

n = Number of years for which cash flow occurs

thus,

a) The future cash flow occurs in 5 years

n = 5

IRR = $[\frac{\ 330,000}{\ 45,000}]^{\frac{1}{5}$ - 1

= 0.4895

or

= 48.95%

b) The future cash flow occurs in 10 years

n = 10

IRR = $[\frac{\ 330,000}{\ 45,000}]^{\frac{1}{10}$ - 1

= 0.2205

or

= 22.05%

c) The future cash flow occurs in 10 years

n = 15

IRR = $[\frac{\ 330,000}{\ 45,000}]^{\frac{1}{15}$ - 1

= 0.1421

or

= 14.21%

d) The future cash flow occurs in 10 years

n = 15

IRR = $[\frac{\ 330,000}{\ 45,000}]^{\frac{1}{20}$ - 1

= 0.1048

or

= 10.48%