Question

Consider the following cash flows on two mutually exclusive projects for the Bahamas Recreation Corporation (BRC). Both projects require an annual return of 15%. Year Deepwater Fishing New Submarine Ride 0 -600,000 -1,800,000 1 270,000 1,000,000 2 350,000 700,000 3 300,000 900,000 as a financial analyst for BRC, you are asked the following questions: a. Based on the discounted payback period rule, which project should be chosen? b. If your decision rule is to accept the project with the greater IRR, which project should you use? c. Since you are fully aware of the IRR rule’s scale problem, you calculate the modified IRR (MIRR) for the two projects. Based on your computation, which project should you choose? d. To be prudent, you compute the NPV for both projects. Which project should you choose? Is it consistent with the MIRR rule?

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Answer 1

	DEEPWATER FISHING:
	YEAR	CASH FLOW	CUMULATIVE CASH FLOW	PVIF at 15%	PV at 15%	Cumulative PV at 15%	PVIF at 25%	PV at 25%	PVIF at 24%	PV at 24%	FVIF at 15%	FV at 15%
	0	$        -600,000	$        -600,000	1.00000	$       -600,000	$        -600,000	1	$      (600,000)	1	$        (600,000)
	1	$          270,000	$        -330,000	0.86957	$         234,783	$        -365,217	0.80000	$         216,000	0.80645	$          217,742	1.32250	$            357,075
	2	$          350,000	$            20,000	0.75614	$         264,650	$        -100,567	0.64000	$         224,000	0.65036	$          227,627	1.15000	$            402,500
	3	$          300,000	$          320,000	0.65752	$         197,255	$            96,688	0.51200	$         153,600	0.52449	$          157,346	1.00000	$            300,000
					$           96,688			$           (6,400)		$               2,716		$         1,059,575
	Discounted payback = 2+100567/197255 =		2.51	Years
	IRR:
	IRR is that discount rate for which NPV = 0. Such a discount rate has to be found out by trial and error. Here, disounting with WACC has given a positive NPV of $96,688. To get to 0
	the discount rate has to be increased. [PV has inverse relationship with discount rate]. With 25% as the discount rate, the NPV is negative--$6400. Further, trial is with 24% and it
	has yielded an NPV of $2716. Now 0 NPV lies between 24% and 25%. Hence, IRR also lies between 24% and 25%.
	By simple linear interpolation, IRR can be found out as:
	IRR = 24%+1%*2716/(2716+6400) =			24.30%
	MIRR:
	With MIRR, the assumption is that the cash inflows for years 1 to 3 are reinvested at WACC. Hence, the FVIF [future value interest factors] have been used to compound the cash
	inflows to t3. The cumulative cash inflow of years 1 to 3 = $1059575. Now the project has only to cash flows. -$600000 at t0 and 1059575 at t3. MIRR is that discount rate which equates
	those two cash flows. Therefore, 1059575 = 600000*(1+MIRR)^3. To solve MIRR it becomes, MIRR =
	MIRR = (1059575/600000)^(1/3)-1 =		20.87%
	NPV				$           96,688
	NEW SUBMARINE RIDE:
	YEAR	CASH FLOW	CUMULATIVE CASH FLOW	PVIF at 15%	PV at 15%	Cumulative PV at 15%	PVIF at 22%	PV at 22%	PVIF at 21%	PV at 21%	FVIF at 15%	FV at 15%
	0	$    -1,800,000	$    -1,800,000	1.00000	$    -1,800,000	$    -1,800,000	1	$   (1,800,000)	1	$    (1,800,000)
	1	$      1,000,000	$        -800,000	0.86957	$         869,565	$        -930,435	0.81967	$         819,672	0.82645	$          826,446	1.32250	$         1,322,500
	2	$          700,000	$        -100,000	0.75614	$         529,301	$        -401,134	0.67186	$         470,304	0.68301	$          478,109	1.15000	$            805,000
	3	$          900,000	$          800,000	0.65752	$         591,765	$          190,630	0.55071	$         495,636	0.56447	$          508,027	1.00000	$            900,000
					$         190,630			$         (14,388)		$             12,582		$         3,027,500
	Discounted payback = 2+401134/591765 =		2.68	Years
	IRR = 21%+1%*12582/(12582+14388) =		21.47%
	MIRR = (3027500/1800000)^(1/3)-1 =		18.92%
	NPV				$         190,630
	ANSWERS:
a]	Based on the discounted payback rule, Deepwater fishing with lower payback should be chosen.
b]	Based on IRR rule, Depwater fishing with higher IRR should be chosen.
c]	Based on MIRR rule, Deepwater fishing with higher MIRR should be chosen.
d]	Based on NPV, New submarine ride with higher NPV should be chosen.
	No, this is not consistent with MIRR rule.