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A rich relative has died and left you a growing perpetuity
A rich relative has died and left you a growing perpetuity. The first payment will occur in a year and will be EUR 2500. Each year after that, you will receive a payment on the anniversary of the last payment that is 2% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 11% per year. 1. What is today's value of the bequest? 2. What is the value of the bequest immediately after the first payment is made?
Expert Solution
Solution :
1.Calculation of today’s value of the bequest :
The formula for calculation of value of a growing perpetuity is
PV = CF1 / ( r - g )
Where
PV= Present value of perpetuity ; CF1 = Cash inflow in one year ; r = discount rate ; g = growth rate ;
As per the information given in the question we have
CF1 = EUR 2500 ; r = 11 % = 0.11 ; g = 2 % = 0.02 ;
Applying the above information in the formula we have the value of the bequest today as
= EUR 2500 / ( 0.11 – 0.02 )
= EUR 2500 / 0.09
= EUR 125,000
Thus the value of the bequest today = EUR 125,000
2.Calculation of value of the bequest immediately after the first payment is made :
The formula for calculation of value of the bequest immediately after the first payment is made
PV = [ CF1 * ( 1 + g ) ] / ( r - g )
Where
PV= Present value of perpetuity ; CF1 = Cash inflow in one year ; r = discount rate ; g = growth rate ;
As per the information given in the question we have
CF1 = EUR 2500 ; r = 11 % = 0.11 ; g = 2 % = 0.02 ;
Applying the above information in the formula we have the value of the bequest immediately after the first payment is made as
= ( EUR 2500 * ( 1 + 0.02 ) ) / ( 0.11 – 0.02 )
= ( EUR 2500 * 1.02 ) / ( 0.11 – 0.02 )
= ( EUR 2500 * 1.02 ) / 0.09
= EUR 2550 / 0.09
= EUR 127,500
Thus the value of the bequest immediately after the first payment is made as = EUR 127,500
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