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example :
Which of the following correctly represents the value of Alphas Start-up Co using the discounted cash flow basis?
$’000
Y1 – 130
Y2 – 180
Y3 – 210
Y4 – 240calculation :
?PV of cash flows = $575(000s)
Value of perpetuity = 240*1.02/(0.11-0.02) = $2,720(000s)
PV of perpetuity = 2,720*0.659 = $1,792(000s)
Total value = $2,367(000s) (575 + 1792)question 1 : the formula of perpetuity factory with growth had changed from (1/r-g) to (1+g/r-g)??
question 2 : the perpetuity factory with growth formula PV = CF @ T1 * 1/r-g, why do we need to time the DF @ Y4
The formula for the perpetuity factor with growth has changed from (1/r-g) to (1+g/r-g). This change accounts for the growth rate of the cash flows in perpetuity.
In the perpetuity factor with growth formula PV = CF @ T1 * 1/r-g, we need to discount the cash flow at Year 4 (CF @ T1) because it represents the cash flow at the beginning of the perpetuity period. Discounting it allows us to calculate the present value of the perpetuity.
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