Question

.Calculate the following: (LG 15-2)

1. Calculate the annual cash flows (annuity payments)

2. from a fixed-payment annuity if the present value of the 20-year annuity is $1 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of the current year.

3. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of five years.

Answer 1

a). Calculating the Annual cash Flow payments where payments began at the end of Current year:-

[1 – (1 + r)"] PresentValue = C* 7

Where, C= Periodic Payments

r = Periodic Interest rate = 10%

n= no of periods = 20

Present Value = $1000,000

$1000,000= C*\frac{[1-(1+0.10)^{-20}]}{0.10}$

1000,000 = C* 1 – 0.14864362802 0.10

C = $117,459.62

So, Annual Fixed Payments are $117,459.62

b). Calculating the Annual cash Flow payments where payments began at the end of 5 years:-

As the payments began at the beginning of the 5th year, we will use Present Value of Annuity due formula with discounted to 5 years.

$Present Value= C*\frac{[1-(1+r)^{-n}]}{r}*(1+r)*\frac{1}{(1+r)^m}$

Where, C= Periodic Payments

r = Periodic Interest rate = 10%

n= no of periods = 20

m = no of years of discount as 1st payment started at the end of year = 5

Present Value = $1000,000

$1000,000= C*\frac{[1-(1+0.10)^{-20}]}{0.10}*(1+0.10)*\frac{1}{(1+0.10)^5}$

$1000,000= C*\frac{[1-0.14864362802]}{0.10}*(1.10)*\frac{1}{1.61051}$

C = $171,972.64

So, Annual Fixed Payments are $171,972.64

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