Question

1. You hold a 6% coupon bond of $100MM with semi-annual payments and exactly four payments remaining to maturity. a.) Show the four future cash flows b.) Calculate the value of the bond if the yield curve is currently flat at 3.5% p.a. and c.) Calculate the duration and volatility of the bond.                                               

2. Your bank has offered you a 5 year loan at 8.4% p.a. to refinance your car. a.)What would your monthly installments be on a $19,000 loan? b.) What would your total payoff balance be if you chose to repay the loan in full on the day after the 45th installment was paid? There is no prepayment penalty.                         

3. Tamarind, Inc. has a bond outstanding with the following characteristics:

Face value:                        $1,000

Years to maturity:             15

Coupon rate                      5.25%

Yield to maturity               4.95%                                                                          (6%)

a. Does this bond sell at a premium or a discount to face value?

b. A US Treasury bond maturing in 15 years has a YTM of 1.95%. What is the spread of Tamarind’s bond?

c. At the time Tamarind issued its bond, the YTM on a T-bond maturing at the same time as Tamarind’s was 4.25%. Tamarind’s bond was issued at par. What was Tamarind’s spread at the time of issuance? What does this information suggest about Tamarind’s financial condition today?

4. Foxtrot Corporation has 10,000 Class A shares and 20,000 Class B shares. Class B shares have 3 times the voting power of Class A shares. You own 50% of the Class A shares and 20% of the Class B shares. a.) What percentage of the company’s shares do you own? b.) What percentage of the votes do you have?

Answer 1

Solution 1:

a.

Future cash flows
Period	Cash Flows (In MM)
1	$3.00
2	$3.00
3	$3.00
4	$103.00

b. Price of bond considering 3.5% p.a yield:

Value of bond will be present value of cash flows discouted at semi annual rate of 1.75%.

Present Value of cash flows
Period	Cash Flows (In MM)	Discount rate	PV Factor	Present Value
1	$3.00	1.75%	0.982801	$2.95
2	$3.00	1.75%	0.965898	$2.90
3	$3.00	1.75%	0.949285	$2.85
4	$103.00	1.75%	0.932959	$96.09
	Total			$104.79

Therefore price of bond considering 3.50% yield is $104.79

c.

Present Value of Weighted cash flows
Period	Cash Flows (In MM)	Period * Cash Flow	Discount rate	PV Factor	Present Value of Weighted Cash Flows
1	$3.00	$3.00	1.75%	0.982801	$2.95
2	$3.00	$6.00	1.75%	0.965898	$5.80
3	$3.00	$9.00	1.75%	0.949285	$8.54
4	$103.00	$412.00	1.75%	0.932959	$384.38
	Total				$401.67

Duration of bond = Present value of weighted cash flows / market price of bond

=$401.67/$104.79 = 3.83

Volatility means the how sensitive a bond is to changes in prevailing interest rates. If rate of interest is changed then price of bond will change by (Duration * change in interest rate)