UNSW Business School
COMM1180
Value Creation
Term 3 2023
Week 8
Value for Investors
Formula Sheet
Simple bond pricing formula
The fair value of a bond with exactly n 6-month periods remaining to maturity, face
value 𝐹, and a coupon rate c% (i.e., a coupon amount of 𝐶 = 𝑐%/2 × 𝐹) and a per
period discount rate of 𝑟 is
𝑃0 = 𝐶
1 − (1 + 𝑟)−𝑛
𝐹
+
(1 + 𝑟)𝑛
𝑟
Constant ordinary perpetuity (e.g. perpetual preference shares):
𝑃𝑉0 =
𝐶
𝑟
Growing perpetuities
Assume that payments grow at constant rate g from one period to the next (typically
𝑔 < 𝑟), e.g., 𝐶2 = (1 + 𝑔)𝐶1 ⋯ 𝐶𝑛 = (1 + 𝑔)𝑛−1 𝐶1 .
Growing perpetuity
If 𝐶1 is the first payment at the end of the first period, then:
𝑃𝑉0 =
𝐶1
𝑟−𝑔
Growing Perpetuity due
If 𝐶0 is the first payment at the beginning of the first period, then:
𝑃𝑉0 =
𝐶0
(1 + 𝑟)
𝑟−𝑔
Return decomposition
Given current price 𝑃0 , future price 𝑃1 , end of period dividend 𝐷1 , the expected return
on equity 𝑟𝑒 can be decomposed into 2 parts, the forward dividend yield and expected
capital gains:
𝑟𝑒 =
𝐷1 𝑃1 − 𝑃0
+
𝑃0
𝑃0
An alternative representation where g is the earnings (dividend) growth rate is:
𝑟𝑒 =
𝐷1
+𝑔
𝑃0
Re-invest to grow
The growth rate of earnings in year t
𝑔𝑡 = Retention Rate%,𝑡−1 × Return on new investments%,𝑡
= 𝑅𝑅𝑡−1 × 𝑅𝑂𝐼𝑡
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