Question

1）Suppose a condo generates $13,000 in cash flows in the first year. If the cash flows grow at 2% per year, the interest rate is 11%, and the building will be sold at the end of 19 years with a value of $90,000, what is the present value of the condo's cash flow?

2）Suppose you save $5,500 at the end of every quarter for your retirement. If you can earn 10% per year (APR) on your investments, how much will you have saved by the time you retire in 15 years?

3）An investment promises to pay you $3,000 per year starting in 6 years. The cash flow from the investment is expected to increase by 2% per year forever. If alternative investments of similar risk earn a return of 13% per year, determine the maximum you would be willing to pay for this investment today.

Answer 1

1]

present value = future value / (1 + interest rate)^{number of years}

present value of the condo's cash flow = sum of present values of cash flows + present value of sale value

present value of the condo's cash flow = $127,864.16

2]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $5500

r = periodic rate of interest. This is (10%/4) = 2.5%. We divide by 4 since we need to convert the annual rate into quarterly rate)

n = number of periods. This is 15 * 4 = 60 (there are 60 quarters in the period)

Future value of annuity = $5500 * [(1 + 2.5%)⁶⁰ - 1] / 2.5%

Future value of annuity = $747,953.74

You will have saved $747,953.74 by the time you retire in 15 years

3]

present value of perpetuity = first payment / (required return - growth rate)

value of investment at end of 5 years = $3,000 / (13% - 2%) = $27,272.73

present value = future value / (1 + interest rate)^{number of years}

value of investment today = $27,272.73 / (1 + 13%)⁵

value of investment today = $14,802.54