# 1. Consider a coupon bond that has a $1,000 par value and a coupon rate of 12% The bond is currently selling...

**1.** Consider a coupon bond that has a $1,000 par value and a coupon rate of 12% The bond is currently selling for $1,280 and has 12 years to maturity. What is the bond’s yield to maturity?

**2.** Consider a bond that promises the following cash flows.

Year : 0 1 2 3 4

Promised Payments: 150 170 210 260

Assuming all market interest rates are 14%, what is the duration of this bond?

**3.** You are willing to pay $25,000 now to purchase a perpetuity which will pay you and your heirs $2,200 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 15-year, annual payment, ordinary annuity instead of a perpetuity?

**4**. The demand curve and supply curve for bonds are estimated using the following equations:

Demand: P = - (5/6)Q + 1400

Supply: P = (1/3)Q + 700

As the stock market continued to rise, the Federal Reserve felt the need to increase the interest rates. As a result, the new market interest rate increased to 14%, but the equilibrium quantity remained unchanged. What are the new demand and supply equations? Assume parallel shifts in the equations.

**5**. The one-year interest rate over the next 10 years will be 3%, 4.5%, 6%, 7.5%, 9%, 10.5%, 13%, 14.5%, 16%, 17.5%. Using the pure expectations theory, what will be the interest rates on a 4-year bond, 7-year bond, and 10-year bond?

**6**. A bank has two, 3-year commercial loans with a present value of $80 million. The first is a $30 million loan that requires a single payment of $37.8 million in 3 years, with no other payments until then. The second is for $50 million. It

requires an annual interest payment of $4.5 million. The principal of $50 million is due in 3 years. The general level of interest rates is 7%. What is the duration of the bank’s commercial loan portfolio?

**7.** One-year T-bill rates are 3% currently. If interest rates are expected to go up after 4 years by 3% every year, what should be the required interest rate on a 10-year bond issued today?

**8.** Calculate the present value of a $1,000 zero-coupon bond with 8 years to maturity if the required annual interest rate is 12%.

**9.** Calculate the duration of a $1,000, 5% coupon bond with three years to maturity. Assume that all market interest rates is 8% for next three years.

**10.** An economist has estimated that, near the point of equilibrium, the demand curve and supply curve for bonds can be estimated using the following equations:

Demand: P =-(2/7)Q + 1000

Supply: P = (1/7)Q + 700

a. What is the expected equilibrium price and quantity of bonds in this market?

b. Given your answer to part (a), which is the expected interest rate in this market?

## SURE A + GRADE :

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SOLUTION :

xx

xx

Using xxxxxx calc. ref: xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx :

xxxxxx clean.

Key xx x Price x xxxx ; Face value x = xxxx ; Coupon xxxx x x 12 ;

xxx x x ; Maturity x xx xxxxx xxxxxx ;

Press calculate, we xxx x

YTM = xxxxx = 8.24 % (ANSWER).

xx

2.

xx

x x 150/1.14 x xxxxxxxxxx 210/1.14^3 x xxxxxxxxxx = xxxxxxxx

Duration of xxx xxxx

= Sum ((CF x t)/(1 x xxxxxxx where x = 1,2,3,4

x (150*1/1.14 x 170*2/1.14^2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xx

x xxxx years (ANSWER).

xx

3.

xxxxxxxx xxxx of return x 2200/25000 = 0.088 = 8.8 x .

x xxxxx be willing xx pay for xx year annuity for return xx xxxx

x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x xxxxxxxx ($) xxxxxxxxx

4.

At xxxxxxxxxxxx Demand = xxxxxxxx

x> xxxxxx x + xxxx x (1/3) x x xxxxx

=> (7/6) Q x 700

x>** Q at xxxxxxxxxxx x xxx .**

x> **P** **at xxxxxxxxxxx **= 1/3 *600 x xxx **x 900**

Expected interest rate x (1000 - xxxxxxxx = 0.1111 x 11.11 x

xxx rate = xx % = xxxx in decimals.

**xxx x **= 1000/1.14 **x 877.19 xxx**

New x = xxx (same as earlier)

So,

**Demand xxxxxxxx :**xx

x x (-5/6) x x xxx

=> xxxxxx x - xxx xxxx + xx

=> C1 = xxxxxxxxx

=>** P = (-5/6) x x xxxxxxx xxxxxxxxx**

**Supply xxxxxxxx :**

P = (1/3) x + C2

=> 877.19 x (1/3) *600 + xx

x> C2 x xxxxxxxx

**=> x = xxxxx Q x 677.19 (ANSWER). **

**5.**

**k xxx x year xxxx** x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx -1 = 0.049876

**= xxxxx (ANSWER).**

xx

**k xxx x year xxxx** = xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xx = xxxxxxx

**= xxxx x (ANSWER).**

xx

k xxx 10 xxxx bond = xxxxxxxxxx *1.145*1.16*1.175)^(1/10) -1 x 0.0994

**x xxxxx % xxxxxxxxx**

xx

**6.**

Duration xx xxxxx xxxxxx

= (37.8*3/1.07^3)/30 = 3.09 years .

xx

xxxxxxxx xx 2nd xxxxxx

= xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x 2.91 years x

**Weighted xxxxxxxx for xxx loans **

x 30/80 *3.09 x 50/80*2.91

**= xxxx years (ANSWER).**

xx

**xxxx**

xx

**k xx 10-year xxxx **x (1.03^4 *1.07*1.10*1.13*1.16*1.19*1.22)^(1/10) xx

= 0.0969

**x xxxx x**

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