Question

4. i. Consider the following demand and supply equations for one-year discount bonds with a face value of $1000.

Bd: P = -0.6Q+1140 Bs: P = Q + 700

1. (6pts) Solve for the equilibrium values of P* and Q*, as well as i*. 6pts.

2. (8pts) Suppose that, as a result of a monetary policy action, the Fed sells 80 bonds that it holds. Assume that Bd and Md are held constant. Write down the new BS equation. Calculate the effect of the Fed’s action on the equilibrium interest rate in this market. 6pts.

ii. (6pts) Using the one period valuation model, assuming a year-end dividend of $1.00, an expected sales price of $100, and a required rate of return of 5%, compute the current price of the stock. 8pts.

Answer 1

(i)

(a)

In bond market equilibrium, Bond demand = Bond supply.

-0.6Q + 1140 = Q + 700

1.6Q = 440

Q = 275

P = 275 + 700 = 975

For 1-year discount bond,

P x (1 + i) = Face value

975 x (1 + i) = 1,000

1 + i = 1.0256

i = 0.0256

i = 2.56%

(b)

Inverse Bond supply function:

Q = P - 700

Sale of 80 bonds increases quantity of bonds supplied (Q) by 80.

New bond supply function: Q = P - 700 + 80 = P - 620

P = Q + 620 (New Bs equation)

Equating new Bs with Bd,

- 0.6Q + 1140 = Q + 620

1.6Q = 520

Q = 325

P = 325 + 620 = 945

For 1-year discount bond,

P x (1 + i) = Face value

945 x (1 + i) = 1,000

1 + i = 1.0582

i = 0.0582

i = 5.82%

Bond interest rate will increase by (5.82 - 2.56)% = 3.26%.

(ii)

Let current bond price be P.

(100 + 1 - P) / P = 0.05

101 - P = 0.05P

1.05P = 101

P = $96.19