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Question:
A firm pays out a constant dividend of 10c in perpetuity. Its cost of equity is 10%.
The value of the dividend stream to an investor is:
10/ 0.1 = 100c
A new project opportunity has arisen;
– The firm would need to cancel the T1 dividend of 10c to pay for it.
– The project should earn 10% return, i.e. the 10c would be worth 10 × 1.1 = 11 c the following year.Solution:
PV = ((10 + 11) × 1.1^-2) + ((10/ 0.1) × 1.1^-2 )
(i.e. the PV of the 21c at T2 plus the delayed perpetuity dividend from T3)
PV = 17.3554 + 82.6446 = 100c
So in theory, provided the firm invests the withheld dividend in projects that at least earn the shareholders’ required return, the investors’ wealth is unchanged and they will not object.
Dividends become a residual – firms only pay a dividend if there are earnings remaining after all positive NPV projects have been financed.
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My Doubt: Could you explain me why the perpetuity dividend “time” from T3 is not -3 but -2 in the PV formula applied. Further T3 was not delayed right as the delayed dividend was from T1, do explain me that as well.
This question and solution is sourced from the Kaplan Study Text.
The reason the perpetuity dividend from T3 is not discounted back to T3 but rather to T2 in the present value formula is due to the timing of cash flows.
The cash flow from the project, which is worth 11c, occurs at T2. Therefore, the total cash flow at T2 is 10c div plus 11c proj return, so 21c at T2.
To calculate PV the perpetuity starting from T3 is considered to begin at T2 because the dividends from T3 onward are based on the assumption that the firm will continue to pay the regular dividend of 10c each year indefinitely.
The formula reflects this by disc the perpetuity back to T2, not T3, thus cash flows are being evaluated at T2. So the cash flow at T2 is 21c, which is discounted back to T0.
The perpetuity starting from T3 is calculated as 10c/0.1, which is also discounted back to T2.This is why the PV formula uses T2 as a ref point for both cash flows. The delayed dividend refers to the T1 dividend that was not paid, but the cash flows from T3 are still evaluated based on the cash flow structure starting from T2.
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