Question

NBN Co will invest in an asset to fund its future purchase of copper wires. This asset is currently trading at $1,835,000. It is expected to generate a monthly cash flow forever that grows at a constant rate of 8% p.a. compounded monthly. The expected cost of capital is 10% p.a. compounded annually. How much would the first cash flow be from such an asset

Answer 1

Growth rate (g) = 8% or 0.08 p.a.compounded monthly.

Now,

Effective annual growth rate =

where g = annual nominal growth rate

n= number of compounding per year = 12

t= years = 1

hence,

Effective annual growth rate =

=>Effective annual growth rate= 0.083 or 8.3 % per annum

Effective monthly growth rate = 0.083/12 = 0.00692 or 0.692 %

Cost of capital = 10% per annum or 0.10 per annum compounded annually.

Effective monthly Cost of capital = 0.10/12 = 0.00833 or 0.833% per month.

Current value of asset =

CF1 = Next month cash flow

g= monthly effective cash flow = 0.00692

c= monthly effective cost of capital = 0.00833

hence,

=>

=> CF1 = $2599.66.

Hence First Month cash flow will be $2599.66 approx.