Question

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows:

Windy Acres			Hillcrest Apartments
Yearly Aftertax Cash Inflow	Probability		Yearly Aftertax Cash Inflow	Probability
30,000	0.2		35,000	0.4
35,000	0.2		40,000	0.2
50,000	0.2		50,000	0.1
65,000	0.2		60,000	0.3
70,000	0.2

Mr. Backster is likely to hold the apartment complex of his choice for about 25 years and will use this period for decision-making purposes. Either apartment can be purchased for $200,000. Mr. Backster uses a risk-adjusted discount rate approach when evaluating investments. His scale is related to the coefficient of variation (for other types of investments, he also considers other measures).

Coefficient of Variation	Discount Rate
0–0.35	5%
0.35–0.40	9	(cost of capital)
0.40–0.50	14
Over 0.50	not considered

a. Compute the risk-adjusted net present value for Windy Acres and Hillcrest Apartments. (Round "PV Factor" to 3 decimal places. Enter the answers in thousands of dollars. Do not round intermediate calculations. Round the final answers to nearest whole dollar.)

	Net present value
Windy Acres	$
Hillcrest Apartments	$

b-1. Which investment should Mr. Backster accept if the two investments are mutually exclusive?

• Hillcrest

• Windy Acres

• Both

• None

b-2. Which investment should Mr. Backster accept If the investments are not mutually exclusive and no capital rationing is involved?

• Windy Acres

• Hillcrest Apartments

• Both

• None

Answer 1

Windy Acres						Hilcrest Apartments					year	PV Factor @ 5% (1/(1.05^n))
Cashflow (x)	Probability (p)	xp	p*((x-mean)^2)		Cashflow (x)	Probability (p)	xp	p*((x-mean)^2)			1	0.952
30000	0.2	6000	80000000		35000	0.4	14000	40000000			2	0.907
35000	0.2	7000	45000000		40000	0.2	8000	5000000			3	0.864
50000	0.2	10000	0		50000	0.1	5000	2500000			4	0.823
65000	0.2	13000	45000000		60000	0.3	18000	67500000			5	0.784
70000	0.2	14000	80000000								6	0.746
	Mean= sum of x*p	50000	250000000			Mean= sum of x*p	45000	115000000			7	0.711
											8	0.677
Std. Deviation					Std. Deviation						9	0.645
=(sum of p*((x-mean)^2))^1/2					=(sum of p*((x-mean)^2))^1/2						10	0.614
=250000000^(1/2)					=115000000^(1/2)						11	0.585
15811.39					10723.81						12	0.557
											13	0.530
Co-efficient of variation					Co-efficient of variation						14	0.505
=Std. Deviation/Mean					=Std. Deviation/Mean						15	0.481
=15811.39/50000					=10723.81/45000						16	0.458
0.32					0.24						17	0.436
											18	0.416
Thus, Discount Rate=					Thus, Discount Rate=						19	0.396
5%					5%						20	0.377
											21	0.359
Risk Adjusted NPV					Risk Adjusted NPV						22	0.342
Year	Expected Cashflow	PV Factor @ 5%	PV		Year	Expected Cashflow	PV Factor @ 5%	PV			23	0.326
0	-$2,00,000	1	-$2,00,000.000		0	-$2,00,000	1	-$2,00,000.000			24	0.310
1-25	$50,000	14.094	$7,04,697.228		1-25	$45,000	14.094	$6,34,227.505			25	0.295
NPV			$5,04,697		NPV			$4,34,228				14.094

b-1 if the two investments are mutually exclusive, Mr. Backster should accept Windy Acres as it has higher NPV.

b-2 If the investments are not mutually exclusive and no capital rationing is involved, Mr. Backster should accept Both as both have Positive NPV.

(Kindly Rate Positively, if found helpful. Thank You :)