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.
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
You are offered an asset with the following cash flows: T 1 ... t-1 t t+1...
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