Question

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A capital investment project will require an initial outlay of $55,000 and is expected to generate an after-tax net cash flow of $7,500 in one year. After-tax net cash flows are then expected to grow at a rate of "g" per year for 5 years, ending 6 years from today In each year after that in perpetuity, after-tax net cash flows are expected to grow at a fixed rate of 1.5% per year. The project's cost of capital is 21%. (a) (4 points) If the terminal value of the project at the end of year 6 (i.e. the present value of all remaining cash flows as of the end of year 6) is $53,486.08, what is the project's NPV? (Hint: first solve for the initial growth rate g) (b) (3 points) Suppose that you have an alternative capital investment project (project B) that requires a $50,000 upfront outlay. This project will generate $2,500 in after- tax net cashflows in one year. In each after that in perpetuity, after-tax net cash flows are expected to grow at a fixed rate of 2.5% per year, what is project B's IRR? Given that the cost of capital for project B is 6.5%, what is the correct decision (accept/reject) according to the IRR rule1? (c) (5 points) Consider another project (project C) which requires an upfront cost of $60,000, and generates a constant S9,000 per year, starting in one year, for 10 years. Assume that project C can be always be replicated at the end of its 10-year life at the same terms, and has the same cost of capital as project B (ie, 6.5%). If you were forced to choose between investing in either project B (from part b) or project C, then determine which of the two projects you should choose to invest in (if any) using the equivalent annual benefit. (Hint: first calculate the NPV of both projects)

Answer 1

	Terminal value = CF6*1.015/(0.21-0.015) = 53486.08
	CF6 = 53486.08*0.195/1.015 =	$          10,275.65
	Further, 10275.65=7500*(1+g)^5
	G = (10275.65/7500)^(1/5)-1 =	6.50%
	Therefore initial growth rate = 6.5%
	NPV of the project = -55000+7500/1.21+7500*1.065/1.21^2+7500*1.065^2/1.21^3+7500*1.065^3/1.21^4+7500*1.065^4/1.21^5+7500*1.065^5/1.21^6+53486.08/1.21^6 =	-10281.533
	Alternatively:
	Year	Cash flows	PVIF at 21%	PV at 21%
	0	-55000.00	1.00000	-55000.00
	1	7500.00	0.82645	6198.35
	2	7987.50	0.68301	5455.57
	3	8506.69	0.56447	4801.80
	4	9059.62	0.46651	4226.38
	5	9648.50	0.38554	3719.91
	6	10275.65	0.31863	3274.14
	Terminal value = 10275.65*1.015/(0.21-0.015) = 53486.08	53486.08	0.31863	17042.31
	Projects NPV =			$   -10,281.53
b)	IRR is that discount rate for which NPV = 0
	Hence, 50000 = 2500/(r-0.025)
	[The formula for PV of growing perpetuity is used]
	Where r = IRR
	r (IRR) = 2500/50000+0.025 =	7.50%
	As the IRR of 7.5% is more than the cost of capital of 6.5%,
	the investment can be accepted per the IRR rule.
c)	NPV of the Project B = -50000+2500/(0.065-0.025) =	$          12,500.00
	EAB = 12500*6.5% =	$                812.50
	NPV of Project C = -60000+9000*(1.065^10-1)/(0.065*1.065^10) =	$            4,699.47
	EAB = 4699.47*0.065*1.065^10/(1.065^10-1) =	$                653.72
	As the EAB of Project C is more it is to be chosen.