Question

Company Upstart goes public. In order to value the company the investment bank that underwrites the offering needs to value Upstart. An important part of this is to determine the cost of capital at which they should discount

Upstart’s future cash flows. The investment bank looks at the data of the industry at the time and finds the following three companies:

Company	Equity Beta	Debt Beta	Debt/Equity Ratio
A	0.9	0.0	20%
B	1.0	0.1	25%
C	2.1	0.3	50%

When Upstart goes public, they will also take on debt to make up 30% of their capital structure. This debt would have a beta of 0.15. The market risk premium is 8% and the risk free rate of interest is 1%.

a) What is a good estimate for Upstart’s cost of capital?

b) What is the expected return on Upstart’s equity after they go public?

Answer 1

We need to calculate the unlevered beta for each of the firm, take an average and then relever the beta for Upstart.

Unlevered beta

Since tax rate, T is not give, we have no other option but to assume the same to be zero. Hence, the formula reduces to:

Company	Equity Beta	Debt Beta	D/E	Bu
	Bl	Bd
A	0.90	0.00	20%	0.7500
B	1.00	0.10	25%	0.8200
C	2.10	0.30	50%	1.5000
			Average	1.0233

Part (a)

Hence, a good estimate for Upstart’s cost of capital = Rf + Bu x Rmp = 1% + 1.0233 x 8% = 9.19%

Part (b)

D / (D + E) = 30%

Hence, D /E = 30% / (1 - 30%) = 0.4286

Levered beta = B_l = Bu x (1 + D/E) - D/E x Bd = 1.0233 x (1 + 0.4286) - 0.4286 x 0.15 = 1.3976

Hence, the expected return on Upstart’s equity after they go public = Rf + B_l x Rmp = 1% + 1.3976 x 8% = 12.18%