Question

a) TD Waterhouse issued today $29,000,000 in bonds, each bond having a par value of $1,000, a coupon rate of 4.50%, and a term to maturity of 9 years. All bonds are issued in Australia therefore, they pay semi-annual interest payments.

Find the Present Value (Annuity) of all coupon payments or cash flow stream if you purchased today one bond only.

b) Now assume that the bond has 5 years to maturity and the market rates are at 3%. What is the price of one bond ONLY with 5 years to maturity? Moreover, if you purchased 35 bonds, what would be the annual interest payment

c) Now if the bond has two years to maturity with a present price of $971.55, find the yield to maturity for the bond at that time.

Answer 1

a) Since the purchase is made on Day 1, the par value will be the Present Value, i.e $ 1,000. Refer below screenshot for the computation.

Principal Answer (a) Period 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 Interest 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 PV 0.98 0.96 0.94 0.91 0.89 0.88 0.86 0.84 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.69 0.67 22.00 21.52 21.05 20.58 20.13 19.69 19.25 18.83 18.42 18.01 17.62 17.23 16.85 16.48 16.12 15.76 15.41 685.05 1,000.00 1,000.00

b) Bond Value with 5 Years remaining will be $ 1,069.17 and annual interest payment for 35 Bonds will be 35 * 1000 *4.5% = $ 1,575. Refer following screenshot for the computations.

Principal Answer (b) Period 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Interest 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 PV at 39 0.99 0.97 0.96 0.94 0.93 0.91 0.90 0.89 0.87 0.86 22.17 21.84 21.52 21.20 20.89 20.58 20.27 19.97 19.68 881.05 1,069.17 1,000.00 Interest Payment for 35 Bonds 1,575

c) YTM is ~ 6.01%. Refer following screenshot for the solution.

0 0 Bond.xlsx - Excel Tell me what you want to do.... - A X Share Data Review View Power Pivot AutoSum = = = Wrap Text General SSY Jabe = File Home Insert Page Layout Formulas Cut Calibri - 10 -A A ES Copy - Paste BI U DO, A Format Painter Clipboard Font Al i x ✓ fox A B C D E E E Merge & Center, $ % 48.09 Insert Delete Format Conditional Format as Cell Formatting Table Styles Styles Clear Sort & Find & Filter Select Editing Alignment Number Cells F G H I J K L M N O P Q R Answer (c) Yield to Maturity Annual Interest + Maturity Value - Market Value)/2 (Maturity Value + Market Value)/2 59.23 985.78 Therefore, YTM 6.01% 3.00% Period 1.00 2.00 3.00 4.00 PROOF Principal Interest 22.50 22.50 22.50 1,000.00 22.50 PV at 3% 0.97 0.94 0.92 0.89 21.84 21.21 20.59 908.34 971.98 60 61 62 Sheet1 + Ready @ J -- - + 1:46 PM * 28/03/2020 100% E 18 A 2

Refer following screenshot for the formulas used:

AS Y ab = Bond.xlsx - Excel 0 0 - A X Share File Home Insert Page Layout Formulas D O Ruler Formula Bar Q Data Review View Power Pivot Tell me what you want to do... Split View Side by Side Hide El Synchronous Scrolling Zoom 100% Zoom to New Arrange Freeze Selection Window All Panes Unhide E Reset Window Position Zoom Window E QE E B Split → Gridlines Headings Normal Page Break Page Custom Preview Layout Views Workbook Views Switch Wind Macros Show Macros Answer (a) Period Principal =C2+1 =C3+1 =C4+1 =C5+1 =C6+1 =C7+1 =C8+1 =C9+1 =C10+1 =C11+1 =C121 =C13+1 =C14+1 t15+1 =C16+1 =C17+1 =C18+1 Interest = 1000'4.5%.12 = 10004.5712 = 1000'4.5.12 = 1000'4.5%/2 = 1000'4.5%/2 = 1000'4.5712 = 1000'4.5212 = 1000'4.5212 = 1000-4.5%/2 = 1000'4.5212 = 1000'4.5%.12 = 1000'4.57.12 = 1000'4.57/2 = 1000'4.5712 = 1000'4.5212 = 1000'4.5%/2 = 1000'4.5712 = 1000'4.57.12 PV = (1/1.0225102 = (1/1.0225503 = (1/1.02255C4 = (1/1.02255C5 = (1/1.0225/C6 = (1/1.02257C7 = (1/1.02257C8 = (1/1.0225509 = (1/1.02251010 = (1/1.02255C11 = (1/1.02257C12 =(1/1.02251 C13 = (1/1.02251C14 =(1/1.02257C15 = (1/1.02251 C16 =(1/1.02257C17 = (1/1.02251C18 = (1/1.02254C19 =E2"F2 =E3'F3 =E4'F4 =E5'F5 =E6'F6 =E7'F7 =E8F8 -E9'F9 = SUMD10:E10)'F10 =SUM(D11:E11) F11 = SUMD12:E12) F12 = SUMD13:E13)'F13 = SUMD14:E14)'F14 =SUM(D15:E15)'F15 =SUM(D16:E16)"F16 =SUM(D17:E17)*F17 =SUMD18:E18)"F18 =SUM(D19:E19)"F19 =SUM( G2:G19) 0 1000 Answer (b) Period Principal =C23+1 =C24+1 =C25+1 =C26+1 =C27+1 =C28+1 =C29+1 =C30+1 =C31+1 Interest = 1000'4.57.12 = 1000'4.52.12 = 1000'4.5212 = 1000'4.5712 = 1000'4.5212 = 1000'4.5%.12 = 1000'4.57.12 = 1000'4.57/2 = 1000'4.5712 = 1000'4.5212 PV at 37 = (1/1.0159023 =(1/1.0159C24 = (1/1.0151025 = (1/1.0159026 = (1/1.0151027 =(1/1.0151028 = (1/1.0151029 =(1/1.0151C30 =(1/1.0151031 = (1/1.0157C32 =E23F23 =E24"F24 =E25 F25 =E26'F26 =E27"F27 =E28 F28 =E29F29 =E30'F30 =SUMD31:E31)"F31 =SUMD32:E32)F32 = SUM(G23:32) Interest Payment for 351 = 35'E322 T Sheet1 Ready @ J -— 78% - + 1:47 PM 28/03/2020 4 2 x 8

Principal Answer (a) Period 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 Interest 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 PV 0.98 0.96 0.94 0.91 0.89 0.88 0.86 0.84 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.69 0.67 22.00 21.52 21.05 20.58 20.13 19.69 19.25 18.83 18.42 18.01 17.62 17.23 16.85 16.48 16.12 15.76 15.41 685.05 1,000.00 1,000.00

Principal Answer (b) Period 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Interest 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 PV at 39 0.99 0.97 0.96 0.94 0.93 0.91 0.90 0.89 0.87 0.86 22.17 21.84 21.52 21.20 20.89 20.58 20.27 19.97 19.68 881.05 1,069.17 1,000.00 Interest Payment for 35 Bonds 1,575