Question

# What is the present value of a growing perpetuity, where the first payment of \$28 occurs...

What is the present value of a growing perpetuity, where the first payment of \$28 occurs 6 months from now, after which payments will grow at the constant rate of 1.2% per annum, and where the interest rate is 11% p.a., compounded semi-annually?

We know that the formula for the present value of growing annuity

PV = D1/(Re-g)

Where D1 is the first payment from today

Re is the required rate of return(interest rate)

g is the periodic growth rate

Given Re = 11% per annum compounded semi annually

Calculation of interest for semi annual period

(1+x)2 = 1.11

1+x = 1.053565

x = 0.05365

Hence Semi annual compounding rate = 5.365%

Similarly we have to find out semi annual growth rate.

(1+y)2 = 1.012

1+y = 1.005982

y = 0.005982

Hence Semi annual growth rate is 0.5982%

Substituting the above rates in the formula we get

= 28/(0.05365-0.005982) = 587.39

Hence the present value of growing perpetuity is \$587.39

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