Question

Someone promises to pay you $1,000,000 every year (at the end of the year) for the next 15 years. The first payment will be one year from today. The relevant effective annual interest rate is 7.0%. What does the time line look like for this problem? What would you pay, today, for this promise?

Answer 1

This is a annuity, where the same amount is to be paid each year for next 15 years.

Amount paid at the end of each year- 1,000,000 $, no. of years = 15 years, Interest rate = 7 %

Amount to be paid today will be the present value of this annuity. PV of the annuity is the present value of all years cashflow discounted at 7 % interest rate.

Present value can be calculated with help of below formula-

where,

FV = future value

PV = present value

r = rate of interest

n = no. of years

Present value of each year cashflow is calculated with help of above formula in below table -

Each year cashflow is discounted based on the year in which it is received. For ex- cashflow of year 1 is discounted for 1 year, for 2nd year it is discounted for 2 year and so on.

year	cash inflow at end of year	Present value	present value of cashflow
1	10,00,000	= 10,00,000 / (1.07)1	934579.4393
2	10,00,000	= 10,00,000 / (1.07)2	873438.7283
3	10,00,000	= 10,00,000 / (1.07)3	816297.8769
4	10,00,000	= 10,00,000 / (1.07)4	762895.212
5	10,00,000	= 10,00,000 / (1.07)5	712986.1795
6	10,00,000	= 10,00,000 / (1.07)6	666342.2238
7	10,00,000	= 10,00,000 / (1.07)7	622749.7419
8	10,00,000	= 10,00,000 / (1.07)8	582009.1046
9	10,00,000	= 10,00,000 / (1.07)9	543933.7426
10	10,00,000	= 10,00,000 / (1.07)10	508349.2921
11	10,00,000	= 10,00,000 / (1.07)11	475092.7964
12	10,00,000	= 10,00,000 / (1.07)12	444011.9592
13	10,00,000	= 10,00,000 / (1.07)13	414964.4479
14	10,00,000	= 10,00,000 / (1.07)14	387817.241
15	10,00,000	= 10,00,000 / (1.07)15	362446.0196
		Total	9107914.005

PV of the annuity is the present value of all years cashflow.

Present value = 9,10,79,14 $ (approx)

Hope it helps!