Assignment 2
1. a. 4 ½ % Bond: 800.00 = 22.50 PVIFA(r/2,10) + 1,000 PVIF(r /2,10); r/2 = 4.817%; YTM =r = 9.634%.
25/8 % Bond: 1,220 = 13.125 PVIFA(r /2,30) + 1,000PVIF(r/2,30); r/2 = 0.52%; YTM = r = 1.04%.
b. 4 ½ % Bond: EAR = (1.04817)2 - 1.0 = .09866 or 9.866%.
25/8 % Bond: EAR = (1.0052)2 - 1.0 = 0.010427 or 1.0427%.
c. Since different securities can have different payment periods (for example, bond interest is paid
semiannually but stock dividends are paid quarterly), direct comparisons can only be made when all yields
are expressed as effective annual rates.
2. Maturity Ask Rate Ask Price in Decimal Bid Price in 32nds Bid Price in Decimal Bid Rate
0.5 5.29% 97.4231 97-13 97.40625 5.326
1.0 5.44% 94.7742 94-24 94.75 5.4662
1.5 5.58% 92.0762 92-01 92.03125 5.613
Remember that prices are quoted for $100 par value.
3. a. With a 10% required reserve ratio the bank has required reserves of $60 ($600 x .1) and excess reserves of
$540. Bank XYZ can lend only to the extent of its excess reserves, in this case, $540.
Bank XYZ
Reserves 60 mln Deposits 600 mln
Loans 540 mnl
b. _
All Banks
Reserves Deposits
Old 48 Old 600
New 12 New 150
Total 60 Total 750
Loans
Old 540
New12/.08=150
Total 690
c.
Bank XYZ
Reserves 72 Deposits 600 mln
Loans 528
1
All Banks
Reserves Deposits
Old 72 Old 600
New -10 New -100
Total 60 total 500
Loans
Old 540
New -12/.12= -100
Total 440
4.a) Yield price is taken directly from the table of spot rates. The yield curve is bumped.
7.00
6.50
6.00
5.50
1 2 3 4 Maturity (6-month period)
b. 1f2? (1+ 0R2/2) = (1+ 0R1/2) (1+1f2/2)
(1+.035) = (1+.03) (1+1f2/2) 1+ 1f2/2 = 1.04 1f2= 0.8 or 8%
2f3 ? (1+ 0R3/2) = (1+ 0R2/2) (1+ 2f3 /2)
(1+.03375) = (1+.035) (1+ 2f3 /2) 2f3 = 0.0625 or 6.25%
3f4? (1+0R4) = (1+ 0R3/2) (1+3f4/2)
(1+.0325) = (1+.03375) (1+ 3f4 /2) 3f4 = 0.057 or 5.75%
c. Expectation theory states that the implicit forward rates are equal to the expected future spot rates if this
theory is correct, then people expect the short term rates to rise to 8% next period, and then fall to 5.751.
Critics: assume risk neutral investors
5. Price = (6)(.96 + .88) + (.88)(100) = 99.04
The yield to maturity is found by solving the following equation for y.
99.04 = 6 /(1 +y )+ 106/(1 +y )2
The solution is y = .06527.
6. c/Price = .07. Substitute Price = 89. c = $6.23. Solve the following equation for ytm.
89 = 6.23 /(1 +ytm )+ 106.23/(1 +ytm)2
The solution is, ytm = .12807.
7 a. Price = 8 PVIF(5%,1) + 108 PVIF(11%,2) = 95.272
b. The stated yield is 8 percent. The current yield is 8/95.272 = 8.397 percent. The yield to maturity is 10.75%
c. The approximation is {8 + (100-95.272)/2}/{(100+95.272)= 10.61%
d. Solve for C using 100 = C PVIF(5%,1)) + (100+C) PVIF(11%,2)
100=0.9524C+(100+C)(0.8116)
100=0.9542C+81.16+0.8116C
C=10.68, Stated yield=10.68% =YTM
2
8. ytm = c/P = 8.5/89 = .0955 Stated yield is 8.5%.
9. a) Since the bond is selling at discount YTM C/par = .08 or 8%
b) Value of all strips =4.0 PVIF (.0355,1)+ 4.0 PVlF (.04,2) + 4.0 PV1F (.03875,3) + 104 PV1F (.0375,4) =
100.89 > 94
Buy bond and strip it to make an arbitrage profit of 100.89-94=$6.89
10. T-account
a. i) Bank
Reserve - 100 Deposit – 100 Required Reserve = -10
Reserve Deficit = 90
ii) Bank
Reserve + 100 Deposit + 100 Required. Reserve. = 10
Excess Reserve = 90
b. Bank A BOC
Reserve + 100 Deposit + 100 Bank A +100
Other Banks -100
Other Banks
Reserve – 100 Deposit – 100
c. i) Bank A
Loan + 100 Deposit + 100 Required = -10 (deficit)
Loan does not add to Reserve
ii) Bank A BOC
Reserve 10 Discount borrowing 10 Discount loan +10 Reserve + 10
iii) Repayment in (i) Bank A BOC
Reserves +100 Reserve +100
Loans -100
Repayment in (ii) Bank A BOC
Reserve -10 Discount Loan -10 Discount Loan -10 Reserve -10
3
d. BOC Bank A
Reserve + 100 Reserve + 100 Deposit + 100
Government Deposit -100
Required. Reserve. = 10
Excess Reserve = 90
