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
90,000	.2		95,000	.2
95,000	.2		100,000	.3
110,000	.2		110,000	.4
125,000	.2		120,000	.1
130,000	.2

Mr. Backster is likely to hold the apartment complex of his choice for about 30 years and will use this period for decision-making purposes. Either apartment can be purchased for $206,000. 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	8	(cost of capital)
0.40–0.50	12
Over 0.50	not considered

  

a.	Compute the risk-adjusted net present value for Windy Acres and Hillcrest. (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	$

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 Both None

Answer 1

a.	Step:1 Find standard deviation of two apartments
	Windy acres
	Year	Cashflow (X)	Probability (P)	P.X	(X-ƩP.X)	(X-ƩP.X)^2	P.(X-ƩP.X)^2
	1	90000	0.2	18000	-20000	400000000	80000000
	2	95000	0.2	19000	-15000	225000000	45000000
	3	110000	0.2	22000	0	0	0
	4	125000	0.2	25000	15000	225000000	45000000
	5	130000	0.2	26000	20000	400000000	80000000
				110000			250000000
	Variance=250000000
	Standard deviation=Sqrt (250000000)=15811.38
	Hillcrest apartments
	Year	Cashflow (X)	Probability (P)	P.X	(X-ƩP.X)	(X-ƩP.X)^2	P.(X-ƩP.X)^2
	1	95000	0.2	19000	-10000	100000000	20000000
	2	100000	0.3	30000	-5000	25000000	7500000
	3	110000	0.4	44000	5000	25000000	10000000
	4	120000	0.1	12000	15000	225000000	22500000
				105000			60000000
	Variance=60000000
	Standard deviation=Sqrt (60000000)=7745.97
	Step:2 Find coefficient of variances
	Coefficient of variance=S.D/ƩP.X
	Windy acres
	Coefficient of variance=15811.38/110000=0.14
	Hillcrest apartments
	Coefficient of variance=7745.97/105000=0.07
	Step:3 Select suitable discount rate
	Windy acres
	Coefficient of variance=0.14
	For Coefficient of variance between 0-0.35,Cost of capital=5%.
	Hillcrest apartments
	Coefficient of variance=0.07
	For Coefficient of variance between 0-0.35,Cost of capital=5%.
	Step:4 Find NPV
	Windy acres
	Cashflow (X)	P.V @5%	Present Value
	90000	0.952381	85714.28571
	95000	0.907029	86167.80045
	110000	0.863838	95022.13584
	125000	0.822702	102837.8093
	130000	0.783526	101858.4016
	Total		471600.433
	Less :Purchase price		206000
	Net present value		265600.433
	Hillcrest apartments
	Cashflow (X)	P.V @5%	Present Value
	95000	0.952381	90476.19048
	100000	0.907029	90702.94785
	110000	0.863838	95022.13584
	120000	0.822702	98724.29698
	Total		374925.5711
	Less :Purchase price		206000
	Net present value		168925.5711
b-1.	Windy acres
	Because of higher NPV
b-2.	Both
	Because NPVs are positive