Question

The City of Albany is considering three proposals to renovate one of its buildings. Company A charges $30,000 upfront payment now and requires three annual payments of $5,000 in the next three years (annual payment coming at the end of each year). Company B offers to get the project done with a total cost of $40,000, which is due now at the beginning of the project. Company C will not bill the city until the project is done in three years. Company C charges the city $50,000 at the end of the third year.

(a) Based on Time Value of Money analysis, if the city uses a discount rate of 5% for analysis, which proposal is the best one and why? (Hint: use annually compounded interests)

(b) If the discount rate changes to 8%, will you change your decision and why?

Answer 1

a)

Present Value, PV = C / (1+r)^t

Where, C is the cash flow, r is the discount rate and t is the time period of the cash flow

Discount rate, r = 5%

Present value of cost of company A = Present value of upfront fee + present value of annual payments

present value of upfront fee = $30,000

present value of annual payments = $5000/(1+5%)¹ + $5000/(1+5%)² + $5000/(1+5%)³

= $5000/1.05 + $5000/1.1025 + $5000/1.157625 = $4,761.90 + $4,535.15 + $4,319.19 = $13,616.24

Present value of cost of company A = $30,000 + $13,616.24 = $43,616.24 ---------------(A)

Present value of cost of company B = Present value of upfront fee = $40,000 ----------------(B)

Present value of cost of company C = Present value of fee after 3 years = $50,000/(1+5%)³ = $43,191.88 ------(C)

Comparing (A), (B) and (C) the present value of company B's proposal is the lowest and hence the proposal of company B should be chosen

b)

Discount rate, r = 8%

Present value of cost of company A = Present value of upfront fee + present value of annual payments

present value of upfront fee = $30,000

present value of annual payments = $5000/(1+8%)¹ + $5000/(1+8%)² + $5000/(1+8%)³

= $5000/1.08 + $5000/1.1664 + $5000/1.259712 = $4,629.63 + $4,286.69 + $3,969.16 = $12,885.48

Present value of cost of company A = $30,000 + $12,885.48 = $42,885.48 ---------------(A)

Present value of cost of company B = Present value of upfront fee = $40,000 ----------------(B)

Present value of cost of company C = Present value of fee after 3 years = $50,000/(1+8%)³ = $39,691.61 ------(C)

Comparing (A), (B) and (C) the present value of company C's proposal is now the lowest and hence the proposal of company C should be chosen now