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Unformatted text preview: AP/ADMS 4540 Financial Management
Fall 2010 Suggested Answers for Assignment 1
Instructor: William Lin ' Problem 1 (5 Step 1: Find appropriate after tax discount rate r.
' = (10.4) ‘ 8% = 4.8% Step 2: Find costs of refunding.
(3)0a11 premium costs = 8% * 30, 000, 000= 2, 400, 000
Floatation Costs = 2, 000, 000
lees PV of future tax savings = (2000000/5)*0.4*PVIFA(4.8%,5) =
400000‘0.4*43535 = 696,560
Cfé) Net Floatation Costs = 2, 000, 000 696, 560= 1, 303, 440
After_ tax additional interest paid on old bonds 2 [1 0. 4]*12%*1/12*30000000
«180, 000
After tax additional interest received on t—bills = (1—0.4)*8X*1/12‘30000000
=120, 000
C3) Net Additional Interest= 180,000  120, 000 = 60,000
Total costs of refunding = Call premium costs + Net Floatation Costs + Net
C') Additional Interest = 2,400,000 + 1,303,440 + 60,000 = 3,763,440 Step 3: Find benefits of refunding 01d yearly coupon payment = 3,600,000
New yearly coupon payment = 2,400,000
Yearly interest savings = 1,200,000 (TD Total benefits = Afterutax PV of savings =
= 1,200,000 * 0.6 * 10.5214 Step 4: Find NPV of refunding
(29 NPV = Total Benefits — Total Costs = 3,811,963
Since NPV >> 0, refunding should clearly proceed. on 000 4' {10 4) *PVIFAM. 8% 15} 1,
= 575, 408 2
7, Problem 2 Note: Figures are in millions.
First, calculate the payments at subsidized stated annual coupon rate of 6%.
Cf) Semiannual interest payments for the first four years = 6%/2 * 100 = 3
(g) Semiannual annuity payments for the final six years 100 / PVIFA(6%/2,12]
100 / 9.954
10.0462
Second, calculate the PV of these payments, discounting at the stated market
annual rate of 10%, and then the grant element.
“PV” of annuity payments after 4 years at 10% PVTFA(10%X2, 12) * 10. 0462 8.8633 * 10. 0362 = 89 0426
PV of these annuity payments today at 10% 89 0426 / 1. 05 = 60. 2675
PV of interest payments today at 10% PUIFAI103/2,8) * 3: 19.3896 (3) PV of payments today 60.2675 + 19. 3896 = 79.5571 Lt) The grant element is then the difference between the loan amount disbursed
(100] and the PV of payments made on the loan (79.6571) = 20,3429 (0 This grant element represents 20 3429/100 or 20. 34293 of the loan, and thus
this loan would not qualify as 00A. The minimum grant element is 25, or the
maximum PV of payments today is 75, for the loan to qualify as ODA. II II  II II (3)1111101, use the method of linear interpolation to get the maximum interest rate
for a grant element of 25, or W of payments being at most 75. Since 6% is too high, try a subsidized interest
the payments as before. rate of 5% and calculate P1! of Cl Semiannual interest payments for the first 4 years = 5W2 * 100 = 2.50
£3 Semiannual annuity payments for the final 6 years at 100 / WIFALSX/Z,12] = 9. 7487
"W" of annuity payments after 4 years at 10% PV of these annuity payments today at 1011.
PV of interest payments today at 10% (3) PV of payments today II II ll If ll PVIFAEIOK/Z, 12) * 9. 7487
86.4052 3 86.4052 / 1.05 = 58.4824
PVIFA[10%/2,8) * 2.50 = 16. 158
58.4824 + 16. 158 = 74.6404 (,1) Since the PV of payments is more than 375, we can begin interpolation: Interest rate PV of payments
6% 79. 6571
C 9) r51. 75. 00
5% '74. 6404 which yields 1‘ = 5.07%. Thus the maximum interest rate is 5.07%. Problem 3 (3.) 19.. Price of bond today = PVIFM3.5%,20]*50 + 1000/1035?" = $1,213.19.
57;). Price of bond 6 years from today = PVIFA(3. 511,831'50 + 1000/0035El == 111,103.11. It) Tlme Pmt PV RV WV
9 0.5 50 48.30910 0.03932 0.01991 1 50 48.87554 0.033474 0.038474 15 50 45.09714 0.037172 0.055759 2 50 43.57211 0.035915 0.071831 2.5 50 42.091305 0.034701 0.080752 ,3 50 40.67603 0.033527 0.100582 3:5 50 39.29955 0.032394 0.113378 4 50 3191058 0.031298 0.125193
(5) 4.5 50 30.00055 11.03024 0.130079 5 50 35.44594 0.029217 0.148080 5.5 50 30.24129 0.023229 0.155261 8 50 33.013916 0.027275 0.153048 6.5 50 31.97021 0.026352 0.17129 7 50 30.03909 0.025461 0.170228 75 50 29.84453 0.0246 0.184501 8 50 28.8353 0.023?03 0.190146 8.5 50 27.06019 0.022904 0.195190 9 50 26.911305 0.022188 0.199691 95 50 26.00778 0.021438 0.203657 10 1050 527.6942 0.434966 4.349656 = 1213.10 1
Durations 6.385319 years
(.2) Voiaumy = 50053197107 = 0.427519
When YTM increases 10 0%, price fans to (1000.42752)% of 1213.19 =
1135.21 (.79 Theduraﬁonwolaﬂlityesﬂmateisclosetome actual prioeof1135.90. You must use duraﬁonalatility to estimate price 201135.21 (1) 1c. r = rf + sumr.) a 5% + 1.2[1556—551) = 17%.
At 3 = 3%, the dividend stream is as follows: Year Dividend PV Today PV After 6 Years
I 3.132 2.67692
2 3.38256 2.47101
3 3.65316 2.28092
4 3. 94542 2. 10547
5 4.26105 1.94351
6 4. 60194 1. 79401
7 4.97009 1.65601 4.24794
8 5.36770 1.52363 3.92118
9 5.79711 1.41104 §.§;954
17.86752 11.78866
C2) Price of one share today = 17.36752 + 70.4.11“a = $34.91
C7.) Price of one share 6 years from today = 11.78866 + 70/1 1'?3 = $55.49 (:2) 1d. Value of 20 shares = 20 * 55.49 = 1109.80 > Value of bond = 1,103.11. CD 1e. 3.. later as value of bond increases.
Cl) 11. later as value of bond increases.
Cl) iii. earlier as value of stock increases.
0) iv. later as value of stock decreases [higher disoount rate).
(A) v. earlier as value of stock increases (lower discount rateL
Pgoblem 4 (5) a. W of arc after 5 years : 1.oz‘°*1.ooo.ooo = 1,218,994.42
_ Real FV of GIC = 1.218.994.42/1.035 = 1,051,515.30 b. As payments are monthly, it is reasonable to aesume compounding period is
a: monthly. As stated, payments C are a regular annuity, paid at month’s end, so:
I: "‘ PVIFA{4%/12.300) = 1,218,994.42
C = 1,2l8,994.42 / 189.4524829 = 6,434.30 c. If prices are expected to grow 3% annually, then the monthly price increase. I, must be:
[6) (144012 = 1+0.03 so 1+1: = 1.03“"2 so 1: = 0.0024662? The first monthly payment C1 can then be found from the growing annuity 6 form113i 1 _ (1.002415627131301
1.00333333
* —............._.........._.. =
L ) C1 [ 0.003333  0_00246627 ] 1,218,994.42 which yields C1 = 4626.39. This monthly payment will grow by 0.246627% each
Cl) month to keep up with inflation. 50 C2 = 4,63?.80 and so on. ...
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