cool question about interest rates

Question

Rob has the opportunity to invest in two different Project Finance projects. The first project is a railroad that will pay monthly interest of $100.00 for 3 years, with a one-year grace period (there is no interest payment in this period) and in the last month, in addition to the interest, there will be an additional payment of $500.00. The other investment is a debenture of a sanitation company that works in bullet format, interest and amortization are paid together once at the end of the debenture, and will pay $3500 at the end of the third year. Assuming an interest rate of 11% per year, what alternative contains the present value of both investments?

a) $3.101,90; $2.559,17

b) $257,12; $2.559,17

c) $3.494,30; $2.629,60

d) $3.774,05; $3.023,43

e) $3.547,00; $2.702,64

Answer 1

This is a classic Corporate Finance question that utilizes the Time Value of money equation for yearly payments, PV = FV / (1+r)^(t). Where PV is the present value, FV is the future value, r is the interest rate, and t is time.

For the first one, we modify the equation to the monthly time value of money, PV = FV / (1+ (r/12) )^(t/12), where t is now in months. Now we sum the months after the grace period for t= 13..48 and r = 0.11,

100/(1+ (0.11/12) )^(13/12) + 100/(1+ (0.11/12) )^(13/12) + ... + 100/(1+ (0.11/12) )^(47/12) = 2772.53

The single additional payment is easier to discount back, 500*(1+.11)^4 = 329.36

The value of the first project is $3101.90

The second project is much easier. We apply the same formula for PV = 3500 / (1+0.11)^(3) = 2559.17

This confirms our choice of A.