Question

10. An asset generates a cash flow of $2 million every 6 years continuing forever, with the first cash flow occurring in 3 years' time. What is the value of the asset if the appropriate discount rate is 8% p.a. compounded semi-annually?

Answer 1

Amount that we will be willing to pay today for buying an asset is nothing but the present value of cash inflows that will be generated by such asset in the future.

Discount Rate: 8% p.a compounded semiannualy. (ie. 4% for 6months)

(6years period means 12 semiannual periods, ie. 4% interest 12 times)

ie. effectively interest rate is 60.1% for 6years

(Working note: Assume $100.

$100+4%+4%+4%... 12 times will give you $160.1

Hence interest for 6years would be $60.1

Thus effective rate of interest for 6years comes to 60.1%)

(Similarly if we calculate for 3years, it would come as 26.53%)

When cashflow from an asset is never-ending, its Present Value = Cash inflow / Interest Rate

Assume current year as YEAR-0

Therefore as on Year 3 (ie. after 3 years), Present Value of cash inflows would be $2million/60.1%

= 2/60.1*100

= $3.328 million (THIS WOULD BE THE 'PRESENT VALUE' AS ON YEAR 3)

Now to calculate the asset's value today (ie. as on year-0) we shall further discount the values for another 3 years as calculated below:

Year Cash Inflow ($million)   Discounting Factor @26.53% Present Value

3 2.00 0.79 (1/1.2653)    1.58

3 3.328 0.79 (1/1.2653)       2.63

     $4.21 million

Therefore the value of the asset today is $4.21 million.