As a result of winning the Gates Energy Innovation Award, you are awarded a growing perpetuity....

As a result of winning the Gates Energy Innovation Award, you are awarded a growing perpetuity. The first payment will occur in a year and will be for $2,685. You will continue receiving monetary awards annually with each award increasing by 4% over the previous award, and these monetary awards will continue forever. If the appropriate annual interest rate is 8.08%, what is the present value of this award?

Solutions

Expert Solution

The first payment will occur in a year and will be for $2,685

annually value to be increasing by 4% means =$2685*4/100 = $107.40

totally increasing this year by $107.40

total value it will be =$2685+$107.40 =$2792.40

again next year same thing it will increasing by 4% of previous award means

= $2792.40*4/100 =$111.70

and value of award come to =$2792.40 + $111.70 =$2904.10

above process to be continue forever the same calculation of award amount.

Present value calculation of the award

In present value calculation we need to consider the factor like interest rate, value and time period

Present value of the first award is first award amount = $2685 time period = 1 (due to time period not available we assume 1) and rate of interest is =8.08% annually

First thing you are present value of the interest rate

PV = Future value *[1/(1+i)n] =$2685[1/(1+0.0808)1] =0.925

=$2685*0.925 then

Present Value: $2,484.27

same calculation will be apply for every year present value calculation only no. of years or period change.

jeff jeffy answered 6 months ago

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