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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