Question

You are offered an asset with the following cash flows:

T	1	...	t-1	t	t+1	t+2	...	Forever
Cash Flow	0	...	0	37	37x(1+g)	37x(1+g)x(1+g)	...

That is, the asset only starts paying in year t and from there on cash flows grow in perpetuity at an annual growth rate given by g. Compute the value of the asset if t = 11 and g = 2% per year. Assume that the discount rate is 7% per year compounded annually. Express your answer with two decimal places.

Answer 1

Given that at t= 11, cashflow will be 37 and it grows at 2% per year for perpetuity. and dicount rate is 7%.

Using the formula of present value of perpetuity, which is PMT/(r-g), where PMT is periodic payment, r is interest rate and g is growth rate, we can calculate present value of perpetuity at t= 10.

Present value of perpetuity at t=10 is PMT(r-g)

= 37(7%-2%)

= 37/0.05

= 740

Now, calculating the present value of perpetuity by discounting it back to t= 0 by discounting it by 10 time periods,

Present value at t=0 is 740/(1+r)^10

= 740/(1+7%)^10

= 740/(1.07)^10

= 376.18

So, Value of the asset= $376.18