Question

Perform an engineering economy analysis of multiple alternatives –decide between renting or buying a house. Determine the present worth of both investments.

Given Information: Buy Rent Cost $500,000 Initial Payment Down Payment: 10% of cost Monthly Payments Security Deposit: $3,500 Rent: $2,500 (increases by 3% per year) First Analysis Objective: Perform an engineering economy analysis of multiple alternatives - decide between renting or buying a house. Explain your answer. Assume: • The TVOM for your own capital is 6% per year • Your planning Horizon is 15 years Your analysis should include a systematic process to compare mutually exclusive alternatives using present worth analysis AND a recommendation of which alternative to choose Mortgage: 15-year fixed • 4% interest / year compounded monthly • End of month payment (End of month payment) $0 Insurance (annual) $400 (increases by 1.5% per year). Assume beginning of the year payments

Answer 1

We will calculate the NPV of cash outflow of both the options and select the option which have least cost:

Option 1: Buying the property

Cost= 500000

Down payment= 10% of Cost i.e $50000

Remaining amount i.e. $ 450000 will be paid as EMI for next 15 years @ $% interest rate compounding monthly:

Calculation of EMI:

[P x R x (1+R)^N] / [(1+R)^N-1]

Here,

P= Loan Amount =450000

R= Monthly Interest rate = 0.04/12 = 0.0033

N= Total No. of installments = 15 x 12 = 180 Months

EMI= [450000 × 0.0033 x (1 + 0.0033)^180 ] / (1 + 0.0033)^180-1

EMI = 1485 × (1.0033)^180 / 1.8094-1

EMI =1485 × 1.8094 / 0.8094

EMI = 2687 / 0.8094

Equal Monthly Installment = $ 3320

NPV of outflow of option 1:

NPV of Down Payment: 50000 x 1 = 50000

NPV of EMI (Compounding factor calculated @ 6%)= 3320 x 118.5035 = 393432

NPV of Insurance =

year (A)	Insurance Amount (B)	Discount Factor(C )	NPV (D)= B X C
0	400	1	400.00
1	406	0.9434	383.02
2	412.09	0.8900	366.76
3	418.27135	0.8396	351.19
4	424.54542	0.7921	336.28
5	430.913602	0.7473	322.00
6	437.377306	0.7050	308.33
7	443.937965	0.6651	295.24
8	450.597035	0.6274	282.71
9	457.35599	0.5919	270.71
10	464.21633	0.5584	259.22
11	471.179575	0.5268	248.21
12	478.247269	0.4970	237.67
13	485.420978	0.4688	227.58
14	492.702292	0.4423	217.92
		Total NPV	4506.85

Total NPV of option 1 = 50000+393432+4507 = $ 447939

option 2: Renting

NPV of outflow under option 2: $ 357559.25 (calculation made in excel spreadsheet):

NPV of Security Deposit= 3500 x 1 = 3500

NPV of rent:

Year	Monthly Outflow(B)	Sum of Discount Factor(C )	Sum of NPV (D)= B X C
1	2500.00	11.62	29047.33
2	2575.00	10.94	28180.63
3	2652.25	10.31	27339.79
4	2731.82	9.71	26524.04
5	2813.77	9.15	25732.63
6	2898.19	8.61	24964.83
7	2985.13	8.11	24219.94
8	3074.68	7.64	23497.28
9	3166.93	7.20	22796.18
10	3261.93	6.78	22116.00
11	3359.79	6.39	21456.11
12	3460.58	6.02	20815.92
13	3564.40	5.67	20194.82
14	3671.33	5.34	19592.26
15	3781.47	5.03	19007.67
Grand Total		118.50	355485.44

	NPV of Security Deposit refunded back = 3500 x 0.4075 =1426.19

Total outflow NPV of option 2 = 3500+355485.44-1426.19 =357559.25

As the cash outflow NPV of option 2 i.e renting is less as compare to option 1 i.e. Buying the property, therefore, option 2 will be preferred.