Capitalized Cost II A wealthy businessman wants to start a p

Capitalized Cost II. A wealthy businessman wants to start a permanent fun d for supporting research sustainability. The donor plans to give equal amounts of money for $100,000 per year directed toward each of the next 5 years, plus one now (i.e., six donations) so that can b e withdrawn each year forever, beginning in year 6. If the fund earns interest at a rate of 8% per year, how much money must be donated each time? CC-$-850,750

Solution

At beginning of year 6 (end of year 5), Present Worth (PW) of future withdrawals = $100,000 / 0.08 = $1,250,000

PW of this amount in year 0 = $1,250,000 x P/F(8%, 5) = $1,250,000 x 0.6806 = $850,750

If required annual donation be D, then

D x P/A(8%, 5) x 1.08** = $850,750

D x 3.9927 x 1.08 = $850,750

D = $850,750 / (3.9927 x 1.08)

D = $197,292.93 (If a negative value is required since donations are cash outflows, value of D = -$197,292.93)

**Since one donation is made at year 0, this is an annuity due and we have to include a multiplication factor of (1 + interest rate)