Question

What interest rate makes $1m a year for 20years (beginning of year payments)economically equivalent to $9million up front?

Answer 1

Present value of the cash flow = 9 million

Annual cash flow (beginning of the year) = 1 million

Time = 20 years

Rate = ?%

This cash flow scheme is shown as

9 million = 1 million + 1 million (P/A, i%, 19)

8 million = 1 million (P/A, i%, 19)

This makes the NPV = 8 m - 1 m (P/A, i%, 19)

For i% = 10%, NPV = 0.36 million

For i% = 11%, NPV = -0.16 million

Hence rate of interest lies between 10% and 11%

Rate of interest = 10% + (11% - 10%)*(0.36/(0.36 + 0.16)) = 10.68%

Hence the rate of interest is 10.68%.