Question

Infrastructure Economics

5) A set of cash revenues starts at $50,000 in the first year and increases each year until no15 years. If the interest rate is 7% (compounded annually), what is the present value of the cash flows if: A. The annual increase is $5,000 per year B. The annual increase is 10% per year 6) An investment of $10,000 is deposited in a bank account which pays 9% annual interest compounded monthly. How much will be in the account after 7 years?

Answer 1

5. Revenue in first year = 50,000

Life = 15 years

Interest Rate = 7%

A. PW if the annual increase is 5,000 per year

PW = 50,000 (P/A, 7%, 15) + 5,000 (P/G, 7%, 15)

PW = 50,000 (9.1079) + 5,000 (52.4461) = 717,625.5

B. PW if the annual increase is 10% per year

PW = 50,000 [1 – (1 + g) ^N (1 + i) ^{– N} ÷ i-g]

PW = 50,000 [1 – (1 + 0.10) ¹⁵ (1 + 0.07) ^{– 15} ÷ 0.07 – 0.10]

PW = 856,711.62

6. Investment = 10,000

Interest = 9% compounded monthly

Monthly interest = 0.09 / 12 = 0.0075

Time = 7 years = 7*12 = 84

FV = 10,000 (1 + 0.0075) ⁸⁴ = 18,732

OR

FV = 10,000 (F/P, 0.75%, 84)

FV = 10,000 (1.8732) = 18,732