Discount Factor

Discount rate/discount factor

The two concepts are very closely tied together. Suppose we have a given discount rate (also known as the interest rate) r. The discount factor, d = 1 / (1 + r). The interest rate is the amount by which the value of an investment will grow every year. The discount factor (which will always be less than 1) is the amount we multiply a future value by to get a present value.

Thus, if we have a future cash flow of $500 at time t, we can use either of these concepts to find the present value of that $500. Using the discount rate:PV = $500 / (1 + r)^t Using discount factors:d = 1 / (1 + r) PV = $500 * d^t Suppose we want to evaluate the present value of $500 received two periods from now. Let's assume that r = 10% Using discount rates: NPV = $500 / (1 + 10%)^2 = $413.22 
Using discount factors: d = 1 / (1 + 10%) = 0.9090 Thus, our NPV = $500 * d^t = $500 * 0.9090^2 = $413.22

You can form a portfolio of two assets, A and B, whose returns have the following characteristics:

Denote by r the expected return of the portfolio. We have r = xA rA + xB rB where xA is the proportion of wealth invested in asset A and x b is the proportion of wealth invested in asset B. Using xB = 1 − xA we get 0.12 = xA × 0.10 + (1 − xA ) × 0.15 implying that xA = 0.60 and xB = 0.40. The variance σ 2 of the portfolio is defined by σ 2 = x 2 Aσ 2 A + x 2 Bσ 2 B + 2(xAx bρABσAσN ) This yields σ 2 = (0.60) 2 × (202 ) + (0.402 ) × (402 ) + 2(0.60)(0.40)(0.50)(20)(40) = 592 and the standard deviation is σ = p 592 = 24.33%.

Omega Corporation has 10 million shares outstanding, now trading at $55 per share. The firm has estimated the expected rate of return to shareholders at about 12 percent. It has also issued long-term bonds at an interest rate of 7 percent. It pays tax at a marginal rate of 35 percent. a) What is Omega’s after-tax WACC? b) How much higher would WACC be if Omega used no debt at all?

1. Assume $200 million debt has been issued V=D+E=750 D/V=$200 mln/$750 mln=0.267 E/V=$550 mln/$750 mln=0.733

after tax WACC= rd (1− Tc )D /V + rE E /V =0.07*(1-0.35)*0.267+(0.12)*0.733=10.01%

1. D=0 WACC= rd D /V + rE E /V =0.07*0.267+(0.12)*0.733=10.67%

The WACC formula seems to imply that debt is “cheaper” than equity – that is, that a firm with more debt could use a lower discount rate. Does this make sense? Explain briefly.

Debt is tax deductible – Initially it is good to use some debt in the capital structure. But there is a point where the advantages of using debt are counterbalanced by their disadvantages, especially when there is a case of a high debt ratio.

Maltese Falcone, Inc., has not checked its weighted average cost of capital for four years.Firm management claims that since Maltese has not had to raise capital for new projectssince that time, they should not have to worry about their current weighted average costof capital since they have essentially?That is a false statement. Maltese is assuming that since it does not have to raise capitalfor new projects, then it has essentially locked in its cost of capital. However, in a liquidcapital market every firm competes for capital everyday since the firm’s investors have the opportunity to sell their investments to other investors. If a firm does not provideinvestors with an ample return, then the investors will sell their investments in the firm,which, in aggregate, will have the effect of actually raising the cost of capital for the firm(since the current price of the securities will move down). Therefore, a firm that ignores 12its current cost of capital by thinking that it has locked in a cost of capital might even be raising its cost of capital by making that incorrect assumption