Question

Your boss asks you to evaluate a project requiring an initial investment of $3,000 and having an infinite life. Revenues and costs occur at the end of the year. At the end of the first year, nominal revenues and nominal costs are projected to be $1,000 and $500, respectively. There is no depreciation, and the tax rate is 30%. The real required rate of return is 10%, and the inflation rate is 4%. Nominal revenues and costs will increase at the rate of inflation (for example, at the end of the second year, nominal revenues and costs will be 4% greater, respectively, than they were at the end of the first year). What is the project's NPV?

Hint: It's a little easier doing the analysis in nominal returns using the perpetuity with growth formula.

	a.	$1,630
	b.	$365
	c.	$500
	d.	$472

Answer 1

Revenue - Cost = 1000 – 500 = 500

After tax profit = 500 x (1-30%) = $350

.

Nominal rate = (1+10%) x (1+4%) -1 = 14.4%

.

Present value of perpetuity = After tax profit x (1+Growth rate) / (Nominal rate - Growth rate)

Present value of perpetuity = 350 x (1+4%) / (14.4% - 4%)

Present value of perpetuity = $3,500

.

Net Present value = - Initial Cost + Present value of perpetuity

Net Present value = - $3,000 + $3,500

Net Present value = $500

Correct option is > c. $500