Question

You have been hired to run a pension fund for TelDet Inc, a small manufacturing firm. The firm currently has $5 million in the fund and expects to have cash inflows of $2 million a year for the first 5 years followed by cash outflows of $ 3 million a year for the next 5 years Assume that interest rates are at 8%. a. How much money will be left in the fund at the end of the tenth year? b. If you were required to pay a perpetuity after the tenth year (starting in year 11 and going 19. through infinity) out of the balance left in the pension fund, how much could you afford to pay?

Answer 1

Answer a:

Current value of fund = $5 million = $5,000,000

Interest rate =8%

Let us calculate first fund value at the end first 5 years:

Annual inflow = $2,000,000

To get fund value at the end of 5 years, we use FV function of excel:

FV (rate, nper, pmt, pv, type)

= FV (8%, 5, -2000000, -5000000, 0)

= $19,079,842.30

Fund value at the end first 5 years = $19,079,842.30

Let us calculate fund value at the end of year 10:

PV at the end year 5 = $19,079,842.30

Annual outflow = $3,000,000

= FV(8%, 5, 3000000,-19079842.30, 0)

= $10,434,745.12

Fund left at the end year 10 = $10,434,745.12

Answer b:

If a perpetuity (annual payment for infinite period) have to be paid from year 11 onward possible amount will be equal to interest earnings = $10,434,745.12 * 8% = $834,779.61

Perpetuity that you can afford to pay = $834,779.61