Question

(Manually Calculate) A newspaper costs $1.00 a day. The interest rate is 6% annually, compounded daily.

a. If the newspapers’ price never changed, what should the newspaper charge for a lifetime subscription assuming you will live for 50 years?

b. What should it charge if you can pass on the subscription to your descendants and they can continue to do the same in perpetuity?

c. What should it charge for a perpetual subscription if the newspaper expects to raise its price by 4% annually (assume daily inflation is 1/365 the annual rate)?

Answer 1

We have:

Daily cost (Pmt) = $1

R= 6%

M= 365

Part A

Here we need to calculate the present value of daily costs.

N= 50 x365 = 18250

r= 6%/365

pmt = $1

we have following formula for PV:

Therefore, Newspaper charge for life subscription would be $5,780.39.

Part B

We have

r= 0.06/365

Pmt = $1

PV of perpetuity = pmt/r

                              = 1/(0.06/365)

                              = 6083.33

Part C

r= 0.06/365

g= 0.04/365

pmt =1

PV of growing perpetuity = Pmt/ (r-g)

                                             = 1/(0.06/365 -0.04/365)

                                             = $18250