Question

Nabil is considering buying a house while he is at university. The house costs 150,000 dollars today. Renting out part of the house and living in the rest over his five years at school will net, after expenses, 1,100 dollars per month. He estimates that he will sell the house after five years for 165,000 dollars. If Nabil's MARR is 18%, compounded monthly, should he buy the house? Use present worth analysis {Perform all calculations using 5 significant figures and round any monetary answers to the nearest cent}.

What is the present worth of this project?   

Should Nabil buy the house?

Answer 1

We have the following information

Initial cost = $150,000

Net annual income = $1100 × 12 = $13,200

Salvage value = $165,000

Interest rate (i) = 18% compounded monthly

Life (n) = 5 years

No. of interest periods per year, (C) = 12

Effective interest rate (R) = ((1 + (i/C))^C – 1

R = ((1 + (18%/12))¹² – 1

R = 19.56% compounded annually

Net Present Worth = – Initial cost + Annual income(P/A, i, n) + Salvage value(P/F, i, n)

Net Present Worth = – 150000 + 13200(P/A, 19.56%, 5) + 165000(P/F, 19.56%, 5)

Net Present Worth = – 150000 + 13200[((1+0.1956)⁵ – 1)/0.1956 (1+0.1956)⁵] + 165000/(1 + 0.1956)⁵

Net Present Worth = – 150000 + (13200 × 3.020) + (165000 × 0.409)

Net Present Worth = – 150000 + 39861.36 + 67538.97

Net Present Worth = – 150000 + 107400.33

Net Present Worth = – ($42,599.67)

Since, the Net Present Worth is negative so Nabil should not buy the house.