The annually compounded discount rate is 13.5%. You are asked to calculate the p

Question

The annually compounded discount rate is 13.5%. You are asked to calculate the present value of a 16-year annuity with payments of $51,800 per year.

Calculate the PV if the annuity payments arrive at one-year intervals. The first payment arrives one year from now.

Calculate the PV if the first payment arrives in six months. Following payments arrive at one-year intervals (i.e., at 18 months, 30 months, etc.).

Calculate the PV if the annuity payments arrive at one-year intervals. The first payment arrives one year from now.

Explanation / Answer

a) PV of annuity =

$51,800(PVIFA13.5%,16)

PV of annuity = $333,113.99

Since this is the preset value at the end of year one to bring it at the beginning of the year we need to discount it back :

PV = $,333,113.99/(1+0.135) = $293,492.50

b) PV if the first payment arrives in six months. Following payments arrive at one-year intervals

Let us have a look at the present value of cash flows 6 months hence:

The first payment will be done ($51,800) + All the subsequent cash flows (15 installments)

PV after six months = $51,800 + $51,800(PVIFA13.5%,15)

PV = $51,800 + $51,800(6.2989)

PV after 6 months = $378,083.02

Now since the cas flows are 6 months hence, we need to discount them and bring them back to the beginning of the year.

PV = $378,083.02(PVIF13.5%,0.5)

PV = $378,083.02(0.9386)

PV of annuity = $ 354,868.723

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