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Unformatted text preview: AP/ADMS 4540 Financial Management
Fall 2009 Suggested Answers for Assignment 1
Instructor: William Lim Problem 1 Step 1: Find appropriate after tax discount rate r.
r — (170.3) * 10% e 7%. [4] Step 2: Find costs of refunding.
Call premium costs = 8% * 30,000,000 = 2,400,000 [2]
Floatation Costs = 1,800,000
less PV of future tax savings = (1800000/5)*O.3*PVIFA(7%,5]= 360000*0.3*4.1002
= 442,822
Net Floatation Costs = 1,800,000442,822 = 1,357,178 [4]
After tax additional interest paid on old bonds = (1—0.3)*12%*1/12*30000000
= 210,000
After tax additional interest received on t—bills = (1—O.3)*8%*1/12*30000000
= 140,000
Net Additional Interest = 210,000 r 140,000 = 70,000 [3]
Total costs of refunding = Call premium costs + Net Floatation Costs + Net
Additional Interest : 2,400,000 + 1,357,178 + 70,000 = 3,827,178 [1] Step 3: Find benefits of refunding
Old yearly coupon payment = 3,600,000
New yearly coupon payment : 3,000,000 Yearly interest savings = 600,000
Total benefits : Aftertax PV of yearly savings = 600,000*(1—0.3)*PVIFA(7%,15)
= 600,000 * 0.7 * 9.1079 : 3,825,318 [41 Step 4: Find NPV of refunding
NPV = Total Benefits — Total Costs = ~1,860.4
Since NPV < 0, refunding should not proceed. [2] MM First, calculate the payments at subsidized interest rate of 6%.
Semiannual interest payments for the first seven years = 3,000,000 [1]
Semiannual annuity payments for the final eight years = 7,961,086.20 [2] Second, calculate the PV of these payments, discounting at the stated
annual rate of 10%. PV of annuity payments after 7 years at 10% = $6,280,660.10
PV of annuity payments today discounted at 10% = 43,577,596.40
PV of interest payments today discounted at 10% = 29,695,800.00
PV of these payments today = 73,273,396,40 [3] The grant element is then the difference between the loan amount
disbursed (=100,000,000) and the PV of payments made on the loan
[=73,273,396.40). Grant Element = 26,726,603.60 Since the grant element is more than 25 million, this loan would qualify
as ODA. [2] Third, use the method of linear interpolation to get the maximum interest
rate for a grant element of 25 million or the PV of payments today being
at most 75 million. Since an interest rate of 6% qualifies the loan as
ODA, we should try an interest rate above 6%, say 7%. [2] First, calculate the payments at subsidized interest rate of 7%.
Semiannual interest payments for the first seven years = 3,500,000 [1]
Semiannual annuity payments for the final eight years = 8,268,483.10 [2] Second, calculate the PV of these payments, discounting at the stated
annual rate of 10%. PV of annuity payments after 7 years at 10% = $9,612,165.70
PV of annuity payments today discounted at 10% = 45,260,233.10
PV of interest payments today discounted at 10% = 34,645,100.00
PV of these payments today = 79,905.333.10 [31 Since the PV of payments today is more than 75 million, we can begin our
linear interpolation to get the maximum interest rate. Interest rate PV of payments today
6 % 73,273,396.40
x % 75,000,000.00
7 % 79,905,333.10 which yields the maximum interest rate X % = 6.26% [4] Problem 3 First, calculate the interest and annuity payments based on the subsidized
annual interest rate of 6%, or quarterly interest rate of 1.5%, for the loan.
Quarterly interest payments over the first year = 1.5% * 10000000 2 150000 [3]
Quarterly annuity payments for next 7 years : lOODOOOO/PVIFA(1.5%,28) = 440011
(where PVIFA{1.S%,28)=22.7267) [5]
Second, discount the payments at the market interest rate of 9%.
"PV" of annuity payments after first year = PVIFA(2.25%,28] * 440011 2 9067671
(where PVIFA(2.25%,28)=20.6G78) [3] 28
PV of theSe annuity payments today = 9067671/1.0225 = 8295498 [2]
PV of the interest payments today 2 PVIFA(2.25%,4]*150000 : 567711
(where PVIFA(2.25%,4) = 3.7847) [3]
PV of future payments on loan = 8863209 [1]
Hence the subsidy = loan disbursed — PV of future payments on loan : 10,000,000 — 8,863,209 = $1,136,791. [3]
P/S‘ Jim Balsillie withdrew his bid for the Phoenix Coyotes on October 1 2009. Problem 4 First calculate the coupon payments per bond 2 8%/2 * 1000 = 40 [2]
Then the price of bond = [40 * PVIFA(5%,20)} + [1000/1.052% = [40 * 12.4622] + 376.89 = 875 38 [2]
Total funds raised = 2000 * 875.38 = 1,750,760. [1] For the second part, first note that the appropriate discount rate is 6%
compounded semiannually (or 3% every six months). [2] Then calculate the costs
of refinancing as follows: Costs of refinancing 2 Issue Costs + Call Premium = 70,000 + 5% of 1000*2000
= 70,000 + 100,000
= 170,000 [5] Next calculate the new coupon payments per bond
= 6%/2 * 1000 = 30 [2]
Hence the semiannual interest savings per bond = 40 — 30 = 10
The present value of these savings per bond = 10 * PVIFA(3%,10) = 10 * 8.5302
2 85.302 [2]
The present value of these savings in total = 2000 * 85 302 : 170,604 which
represent the benefits of refinancing. [2] Since the interest savings exceed the Costs of refinancing, refunding should
proceed. [2] Problem 5 a. The required rate of return on Deerhead stock r = rf+B(rm—rf) =
10+1.5(18—10] = 22%. [4]
Since the current dividend is $3.75, which means that the next dividend
is 3.75*[1+15%) = 4.31. [2]
Hence the current price of a share of Deerhead stock P : D1/[rug]
= 4.31/(0.2240.15)
= 61.61. [2] 12 88. [2] b. Dividend payment 7 years from today = 3.75*1.25*1.15 Price of a share of Deerhead stock 6 years from today = P5 = D7/r—g
: 12.88/[0.ZZeO.15) = 183.96 [2}
PV today of P5 = 183.96/1.226 = 55.79 [2]
Dividend payment one year from today = D1 = 1.2*3.75 = 4.50
1 — %$§)6 1 — (%4%2J6
PV today of dividends for next 6 years = D1*[——F—:—ée——] = 4.50*[ 57§§—:L6T§ ]
= 4.50*4.72 = 21.24 [3] Price of a share of Deerhead stock today = 55.79 + 21.24 = 77.03. [1} The increase in price is $77.03m61.61=$15.42 per share. Therefore the
shareholders should be willing to pay at most $15.42 times the number of
shares outstanding for this advertisement. [2] ...
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