Download Bond Valuation and Dividend Growth Model and more Lecture notes Mathematical finance in PDF only on Docsity!
TCCB – problem
EX: Soo Lee imports issued 1000 bonds with 17-year bonds 2 years ago at a coupon
rate of 10.3 percent. The bonds make semiannual payments. These bonds currently
sell for 102 percent of par value. What is the yield to maturity? Verify that your
answer is correct. (the yield to maturity is r)
Bond value = C x (1- 1/〖(1+r/2)〗^(t2) )/((r/2))+ (Face bond value)/〖(1+r/2)〗^(t2)
(1.0001,02) =((1.0000,103))/2 x (1- 1/〖(1+r/2)〗^(15*2) )/((r/2))+
1.000/〖(1+r/2)〗^(15*2)
=> r = 0,1004 = 10,04%
Cách 2: Bond price =
FV ∗ coupon 2
YTM
− 2 n YTM 2
+ FV ( 1 +
YTM
− 2 n
FV mình k biết => auto khoán = 1000
Bond price = 1000*102% = 1020
YTM
− 30 YTM 2
YTM
− 30
EX: Jen’s Fashions is growing quickly. Dividends are expected to grow at a 19
percent rate for the next 3 years, with the growth rate falling off to a constant 8
percent thereafter. The required return is 12 percent and the company just paid an
$3.80 annual dividend. What is the current share price?
D 0 =3.8 D 1 = D 0 ∗( 1 +0.19)=3.8∗( 1 +0.19) =4.522 D 2 = D 1 ∗( 1 + 0.19)=4.522∗( 1 +0.19) =5.
D 3 = D 2 ∗( 1 +0.19)=4.404∗( 1 +0.19)=6.404 D 4 = D 3 ∗( 1 +0.08 )=6.404∗( 1 +0.08) =6.
P 3 =
D 4
r − g
P 0 =
D 1
1 + r
D 2
( 1 + r )
2 +^
D 3
( 1 + r )
3 +^
P 3
( 1 + r )
3 =^
2 +^
3 +^
Scott is considering a project that will produce cash inflows of $2,100 a year for
4 years. The project has a 12 percent required rate of return and an initial cost of
$6,000. What is the discounted payback period? ( đã thi)
Discounted payback period:
Year 1 2 3 4
Cash flow 2100/(1+12%)^1 2100/(1+12%)^2 ,...... ,.....,
Sum of the 4-year cash flow = 6378.43 > 6000 => Should take the project
Cách 2:
Year
Discounted pay-back period
Cash flow Y1 =
( 1 + r )
1 =^
Cash flow Y2 =
( 1 + r )
2 =^
Cash flow Y3 =
( 1 + r )
3 =^
Question 1: ABC corporation shows the following information on its 2020 income statement: sales= $267,000, costs= $148,000, other expenses=$8,200; depreciation expense=$17,600; interest expense=$12400, taxes=$32,620, dividends=$15,500. Firm also issued $6,400 in new equity during 2020 and redeemed $4,900 in outstanding long-term debt. a. What is the 2020 operating cash flow? b. What is the 2020 cash flow to creditors? Cash flow to stockholders? c. If net fixed assets increased by $25,000 during the year, how does NWC change? Solution: a. EBIT = Sales - Costs - Other Expenses - Depreciation expense EBIT = $267,000 - $148,000 - $8,200 - $17,600 = $ Operating Cash Flow = EBIT + Depreciation Expense – Taxes = $93200 + $17,600 - $32,620= $78, b. Cash flow to creditors = Interest – Net new LTD = $12,400 – (-4900) = $17, Cash flow to stockholders= Dividends – Net new equity = $15,500 - $6,400 = $9, c. We know that CFA = CFC + CFS, so: CFA = $17,300 + 9,100 = $26, CFA is also equal to OCF – Net capital spending – Change in NWC. We already know OCF. Net capital spending is equal to: Net capital spending = Increase in NFA + Depreciation = $25,000 + 17,600 = $42, Now we can use: CFA = OCF – Net capital spending – Change in NWC $26,400 = $78,180 – 42,600 – Change in NWC
Change in NWC = $9, This means that the company increased its NWC by $9,180. Question 2: A firm has the following marginal tax rate information: a. Why do you think the marginal tax rate jumps up from 34% to 39% at a taxable income of $100,001 and then falls back to a 34% marginal rate at a taxable income of $335,001? b. Compute the average tax rate for a corporation with exactly $335,001 in taxable income. Does this confirm your explanation in part (a)? What is the average tax rate for a corporation with exactly $18,333,334 in taxable income? Is the same thing happening here? Solution: a. The marginal tax rate measures the amount of tax applied on income that goes over the tax bracket limits. Tax brackets are progressive, so the IRS taxes income at different rates. This ensures that higher-income earners pay their fair share in taxes. The change in marginal tax rate in this case leads average tax rates to catch up to marginal tax rates, thus eliminating the tax advantage of low marginal rates for high income corporations. b. For a corporation with exactly $335,001 in taxable income Tax bill = 0.15($50,000) + 0.25($25,000) + 0.34($25,000) + 0.39($235,000)
- Monthly_ m = 12
- Infinite: EAR = eq- Using above formula, we can get the solution as below: **APR Number of Times Couponed EAR
%** Semi annually 12.4% 7% Quarterly **7.19%
%** Monthly 11.7% 10% Infinite 10.52% Question 6: Beginning three months from now, you want to be able to withdraw $2,500 each quarter from your bank account to cover college expense over the next four years. If the account pays 0.47% interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years? Solution: The cash flows are simply an annuity with four payments per year for four years, or 16 payments. We can use the PA equation: PV = $ 2,500 x [ (1 - 1 / (1+0.0047)16 ) / 0.0047 ] = $ 38,446. Question 7: Suppose you are going to receive $13,500 per year for five years. The interest rate is 8.4% a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due?
b. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are annuity due? c. Which has the highest present value (future value), the ordinary annuity or annuity due? Solution: a. PV = $13.500[(1- (1/ (1+ 0.084)^5)/0.084] = $53,338. The present value of the payments if they are an annuity due: PV (due) = PV(1+r) = $53,338.08(1+0.084) = $57,818. b. if the payments are an ordinary annuity FV= $13,500[((1+0.084)^5 – 1)/0.084] = $79,833. if the payments are annuity due FV(due)= FV(1+r) = $79,833.24(1+0.084) = $86,539. c. Assuming a positive interest rate, the present value of an annuity due will always be larger than the present value of an ordinary annuity. Each cash flow in an annuity due is received one period earlier, which means there is one period less to discount each cash flow. Assuming a positive interest rate, the future value of an ordinary due will always higher than the future value of an ordinary annuity. Since each cash flow is made one period sooner, each cash flow receives one extra period of compounding. Question 8: Prepare an amortization schedule for a five-year loan of $65,000. The interest rate is 7% per year and the loan calls for equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan.
b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate.
Bài 1: y hệt ex2.
Bài 2: Bond price
Bond price = FV ∗ coupon ∗(
1 −( 1 + YTM )
− n
YTM )
+ FV ( 1 + YTM )
− n
YTM
− 2 ∗16. YTM 2
YTM
− 2 ∗16.
Xong tính YTM
management numbers of payback and discounted payback periods for both projects are 3
years. Which project should you accept based on NPV/ Payback/ Discounted Payback
Analysis.
