Question

The P/E ratio on a stock market is 12. The underlying real earnings growth rate is 1.6%, at a constant long-run inflation rate of 2.7%. What is the firm's nominal long-run cost of capital?

Carry out calculations to at least 4 decimal places. Enter percentages as whole numbers. Example: 3.03% should be entered as 3.03. Do not include commas or dollar signs in numerical answers.

Answer 1

Cost of Capital is required rate of return of an Investor to bear certain amount of risk. In other words, this is minimum rate of return than an investor required to invest.

P/E ratio is the ratio of Price of share and Earning Per share, this ratio indicates how much an investor willing to pay for earning $ 1. The inverse of P/E i.e E/P is also known as Return on Equity (ROE).

We have following information provided -

P/E ratio = 12

Growth rate (g) = 0.016

Long-run inflation rate = 0.027

Now, as per constant-growth Earning model

$Cost of Capital (K_{e})=\frac{E}{P}+g$

Where,

Ke = Cost of capital

E = Earning per share

P = Price of share

g = Growth rate

P/E = 12

thus, E/P = 1/12 = 0.0833

Cost of Capital (Ke) = E/P + g

= 0.0833 + 0.016

= 0.0993

Cost of Capital without adjusting Inflation is called Nominal Interest rate and Cost of Capital adjusted with Inflation is called Real Interest rate.

As the question requires to provide Long-run Nominal Interest rate, Thus we need not adjust cost of capital with inflation.

Therefore, Firm's Nominal Long run Cost of Capital (Ke) is 0.0993