In: Finance
Q1 ) A 1000$ , 6% annual coupon treasury bond that is quoted in the newspaper at 103:5 Ask, coupon interest is paid semi-annually , it has been 130 days since the last coupon payment, half year is 182.5 days , find :
a) What is the accrued interest on the bond on the bond ?
b) If you are to buy the bond , what is the invoice price, how much would you pay for the bonds in other word ?
Q2 ) The Sami’s firm common stock most recent dividends were 2$ per share, dividends are to grow at 8% a year for 3 years (2016,2017,2018) , at the end of year 2018, dividends are to grow at 5% for the foreseeable future , required rate of return is 15% .
What is the shares true value now and that is at the beginning of year 2016 ?
Q1 ) A 1000$ , 6% annual coupon treasury bond that is quoted in the newspaper at 103:5 Ask, coupon interest is paid semi-annually , it has been 130 days since the last coupon payment, half year is 182.5 days , find :
a) What is the accrued interest on the bond on the bond ?
accrued interest = earned interest but not recieved
Here, 130 day interest are earned but not recieved
calculate 130 days interst
interest is paid semi-annually = 1000 * 6% / 2 = 30 182.5 days interest is = $ 30
130 days interst accrued = 30 / 182.5 * 130 = $ 21.37 per bond
b) If you are to buy the bond , what is the invoice price, how much would you pay for the bonds in other word ?
Bond price is the Present avlue of its interest to receive and its par value received at end discounted with at its yield to maturity
yield to maturity = 60 /1035 = 0.058 = 5.8%
and also convert the YTM to remaining period of bond of 182.5 - 130 = 52.5 = 5.8 / 365 * 52.5 = 0.83%
so 52.5 days iterest = 30 - 21.37 = $ 8.36
Par = 10000
bond price = PV of Interest + PV of Par
bond price = 8.36 / ( 1 + 0.83%)1 + 1000 / ( 1 + 0.83% )1
bond price = 8.36 / 1.0083 + 1000 / 1.0083 = 8.29 + 991.77 = 1000
how much would you pay = 1000
Q2 ) The Sami’s firm common stock most recent dividends were 2$ per share, dividends are to grow at 8% a year for 3 years (2016,2017,2018) , at the end of year 2018, dividends are to grow at 5% for the foreseeable future , required rate of return is 15% .
What is the shares true value now and that is at the beginning of year 2016 ?
It calculated using The Two-Stage Dividend Discount Model
End of yewar | Dividend (Dn) | PV factor @ 15% |
PV of dividend Dn * PV factor @ 15% |
2016 | 2 + 8% = 2.16 | (1 / 1 + 15%)1 = 0.8696 | 1.8783 |
2017 | 2.16 + 8% = 2.3328 | (1 / 1 + 15%)2 = 0.756 | 1.7636 |
2018 | 2.3328 + 8% = 2.52 | (1 / 1 + 15%)3 = 0.65758 | 1.534 |
Total PV of future dividends - Years 2016 through 2018: $ 5.176
After period 2018 dividends are to grow at 5% for the foreseeable future
Here
Project the dividend for Year 2019 by multiplying the Year 2018 dividend by (1 + the growth rate for Year
4), which is = 2.52 + 5% = 2.646
Pretend that Year 2019 is Year 1 and so the end of Year 2018 is Year 0. Use the Constant Growth Model
to calculate the value of the stock at the end of Year 2018, assuming a required rate of return of 15% and an
annual growth in dividends of 5% going forward from the end of Year 2018 beginning with Year 2019
P2018 = D4 / R − G
P2018 = 2.646 / 15 - 5 = 2.646 / 10% = 26.46
The $26.46 present value calculated in occurs at the end of Year 2018, not at Year 2016.
Therefore, $26.46 must be discounted back 3 years to Year 0. Discount it back as a single sum that will be
received in 3 years. The present value factor for 3 years at 15% is 0.65758 , so the present value as of Year 2016
of the dividends to be received beginning at the end of Year 2019 and continuing indefinitely is
= 26.46 * 0.65758 = $ 17.40
fair value at Year 2016 = $ 5.176 + $ 17.40 = 22.576 = $ 22.58
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