Question

No excel pleae! I am trying to learn the math for the exam! Thank you!!

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

Answer 1

Future value= Present value*(1+rate)^n

PV of cash inflows= PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

= 2*(1-1/(1+8%)^5)/8%

= 2*3.992710037

= 7.985420074 million

PV of cash outflows at year 5= Annuity*(1-1/(1+rate)^number of terms)/rate

= 3*(1-1/(1+8%)^5)/8%

= 3*3.992710037

= 11.97813011 million

PV of cash outflows now=  11.97813011/ 1.08^5

= 8.152114085 million

Total Present value now= Initial amount+ PV of inflows-PV of outflow

= 5+7.985420074 -8.152114085

=4.833305989 million

Amount accumulated at year 10= 4.833305989* 1.08^10

=10.43474512 million

= $ 10434745.12

ii) Amount of annuity given after year 10 = Present value of the fund at time 10* rate

= 10434745.12* 8%

=$ 834779.61