FIXED INCOME VALUATION & MANAGEMENT CLASSWORK SOLUTIONS

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Augustine Poole
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1 FIXED INCOME VALUATION & MANAGEMENT CLASSWORK SOLUTIONS. Conversion rate is shares per bond. Market price of share ` 80 Conversion Value x ` 80 = ` 0 Market price of bond = `. Premium over Conversion Value (` - ` 0) = 00.% 0 a. If the yield of the bond falls the price will always increase. This can be shown by following calculation. IF YIELD FALLS TO 6% Price of yr. bond ` 80 (PVIFA 6%, yrs.) + ` 000 (PVIF 6%, yrs.) ` 80 (.)+ ` 000 (0.) ` `.00 = `,08.96 Increase in year s bond price = ` 8.96 Current price of 0 year bond ` 80 (PVIFA 6%, 0) + `,000 (PVIF 6%, 0) ` 80 (.) + `,000 (0.) ` `.00 = ` 9.60 So increase in bond price is ` 9.60 PRICE INCREASE DUE TO CHANGE IN PV OF PRINCIPAL yrs. Bond `,000 (PVIF 6%, ) `,000 (PVIF 8%, ) `,000 (0.) `,000 (0.68) `.00 ` = ` & change in price due to change in PV of Principal (` 66/ ` 8.96) x 00 = 8.6% 0 yrs. Bond `,000 (PVIF 6%, 0) `,000 (PVIF 8%, 0) `,000 (0.) `,000 (0.) `.00 `.00 = ` & change in price due to change in PV of Principal (` 98/ ` 9.60) x 00 =.68% PRICE CHANGE DUE TO CHANGE IN PV OF INTEREST yrs. Bond ` 80 (PVIFA 6%, ) ` 80 (PVIFA 8%, ) ` 80 (.) ` 80 (.99) ` 6.96 ` 9. = `.

2 % change in price ` % ` yrs. Bond ` 80 (PVIFA 6%, 0) ` 80 (PVIFA 8%,0) ` 80 (.) ` 80 (9.8) ` 9.60 ` 8.60 = ` ` & change in price = 00.9% ` 9.60 b. Duration in the average time taken to recollect back the investment Years (A) 6 Coupon Payments (`) Redemption (`) Total (`) (B) 0 % (`) (C) (A )x(b)x (C) (`) ,. =,09.9 ABC ` 09.9 Duration.098 years Purchase Pr ice ` 000 c. If YTM goes up to 0%, current price of the bond will decrease to ` x PVIFA (0%,6) + ` 000 PVIF (0%,6) ` ` 6.00 = ` Year (A) 6 Inflow (`) (B) 0 0% (C) (A )x(b)x (C) (`) ,60.88 =,66. New Duration `,66./ ` =.0 years The duration of bond decreases, reason being the receipt of slightly higher portion of one s investment on the same intervals.

3 . Step - I : Calculation of initial outlay:- ` (million) a. Face value 00 Add:-Call premium Cost of calling old bonds b. Gross proceed of new issue 00 Less: Issue costs 6 Net proceeds of new issue 9 c. Tax savings on call premium and unamortized cost 0.0 ( + 9) 6. d. Initial outlay = (a - b - c) =. Step - II : Calculation of net present value of refunding the bond:- Saving in annual interest expenses ` (million) [00 x (0. 0.0)] 6.00 Less:- Tax saving on interest and amortization 0.0 x [6 + (9-6)/6].9 Annual net cash saving.0 Present value of net annual cash saving [.0 PVIFA (%, 6 yrs)] 9.0 Less:- Initial outlay. Net present value of refunding the bond.60 Decision: The bonds should be refunded. Suppose X be the maximum amount Mr. Y can pay for Treasury Bill. Then, `,000 X `,000 9 `,000 - X = `. X = `,9.6. (i) (ii) (iii) Rate used for discounting shall be yield. Accordingly ZCB shall fetch: `,8 The day count basis is actual number days / 6. Accordingly annualized yield shall be: FV Pr ice Yield 6.86% Pr ice No. of days Note: Alternatively, it can also computed on 60 days a year. Price GOI 0 would fetch = ` 0. PVAF(8%, 0) + ` 00 PVF (8%, 0) = ` 0. x 6. + ` 00 x 0.6

4 (iv) = `.86 + ` 6. = ` 8.8 Price GOI 08 Bond would fetch: = ` PVAF (%, 0) + ` 00 PVF (%, 0) = ` x 8. + ` 00 x 0.66 = = First we shall find the Conversion Value of Bond CV = C (+g) n x R Where: C = Current Market Price g = Growth Rate of Price R = Conversion Ratio n = No. of years Accordingly, CV shall be = `.0 x.0 x = `.0 x. x = ` 0.98 Value of Bond if Conversion is opted = ` 00 x PVAF (%, ) + ` 0.98 PVF (%,) = ` 00 x.0 + ` 0.98 x 0.69 = ` ` 6.8 = ` 98.0 Since above value of Bond is based on the expectation of growth in market price which may or may not as per expectations. In such circumstances the redemption at premium still shall be guaranteed and bond may be purchased at its floor value computed as follows: Value of Bond if Redemption is opted = ` 00 x PVAF (%, ) + ` 00 PVF (%,) = ` 00 x.0 + ` 00 x 0.69 = ` ` 69.9 = ` 00.. (i) Current Market Price of Bond Time CF PVIF 8% PV (CF) PV (CF) PV (CF) i.e. P 0 = Say `.00 (ii) Minimum Market Price of Equity Shares at which Bondholder should exercise conversion option:.00 Rs (iii) Duration of the Bond Year Cash flow 8% Proportion of bond value Proportion of bond value x time (years)

5 (i) Stock value or conversion value of bond 0 = ` 0 (ii) Percentage of the downside risk ` 6 ` ` 6 ` 0. or.% or 0. or.% ` ` 6 This ratio gives the percentage price decline experienced by the bond if the stock becomes worthless. (iii) Conversion Premium Market Price Conversion Value 00 Conversion Value ` 6 ` % ` 0 (iv) Conversion Parity Price BondPrice No.of Shares on Conversion ` 6. 0 ` This indicates that if the price of shares rises to `. from ` the investor will neither gain nor lose on buying the bond and exercising it. Observe that `. (`. `.00) is 0.% of `, the Conversion Premium. 9. ` (i) Current yield = 0. or.% ` 90 6 YTM can be calculated as follows: Redemption value Face Value Coupon YTM n Redemption value Face Value = 8.% 00 90

6 0. (i). (ii) The duration can be calculated as follows: Year Cash Flows 8.% 8.% Proportion of NCD value Duration =.6 half years i.e..68 years. (iii) Realized Yield can be calculated as follows: (ii) R R /0 R or 6.80% for half yearly and.6% annually. 90 Proportion of NCD value time If the current interest rate is 8%, the company will not extent the duration of Bond and the maximum amount the investor would ready to pay will be: =,000 PVIAF (8%, 6) + 0,000 PVIF (8%, 6) =,000 x.6 + 0,000 x 0.60 =,6 + 6,00 = 0,9 If the current interest rate is %, the company will extent the duration of Bond. After six years the value of Bond will be =,000 PVIAF (%, 6) + 0,000 PVIF (%, 6) =,000 x. + 0,000 x 0.0 =, +,0 = 9,8 Thus, potential loss will be 9,8-0,9=, a. Conversion Value of Debenture = Market Price of one Equity Share X Conversion Ratio = ` X 0 = ` 0 b. Market Conversion Price Market Pr ice of Convertible Debenture Conversion Ratio 6

7 ` 900 ` 0 0 c. Conversion Premium per share Market Conversion Price Market Price of Equity Share = ` 0 ` = ` d. Ratio of Conversion Premium Conversion premium per share ` 0% Market Pr ice of Equity Share ` e. Premium over Straight Value of Debenture Market Pr ice of Convertible Bond % Straight Value of Bond ` ` 0 f. Favourable income differential per share Coupon Interest from Debenture Conversion Ratio Dividend Per Share Conversion Ratio ` 8 0 ` `.8 0 g. Premium pay back period Conversion premium per share `. years Favourable Income Diffential Per Share `.8. The appropriate discount rate for valuing the bond for Mr. Z is: R = 9% + % + % = % Time CF PVIF % PV (CF) PV (CF) PV (CF) i.e. P 0 = Since, the current market value is less than the intrinsic value; Mr. Z should buy the bond. Current yield = Annual Interest / Price = 0 / 0.86 =.6% RR Pr ice Coupon YTM n RR Pr ice where RR = Redemption Value =.9%

8 ` 0, 000 ` 9, Investment Rate = 0.0 i.e..% ` 9, 90 9 ` 0,000 ` 9,90 60 Discount Rate = 0.0 i.e..% ` 0, Present Value of Debenture Year Cash Outflow (`) PVF@6% Present Value (`) The formula for the duration of a coupon bond is as follows: YTM tc YTM t YTM YTM c YTM YTM Where YTM = Yield to Maturity c= Coupon Rate t= Years to Maturity Accordingly, since YTM =0.6 and t= c c c c c c c =.086 c c = C = c = 0. Where c = Coupon rate Therefore, current price = `(,00,000/- x 0. x.68 +,00,000/- x 0.0) = `96,/-. Alternatively, it can also be calculated as follows: Let x be annual coupon payment. Accordingly, the duration (D) of the Bond shall be Year CF PVIF 6% PV (CF) PV (CF) 000 x x x x x X x 0.x 0.6x 0.x 0.6x x 000 8

9 0.86x 0.x 0.6x D.68x x x x 0.6x 0.0x x x x 000.9x x 000 x = `,98 i.e..98% say % Accordingly, current price of the Bond shall be: =,00, PVAF (6%, 6) +,00,000 PVF (6%, 6) =, ,00, = ` 96, 6. Duration of Bond X Year Cash flow 0% Proportion of bond value Proportion of bond value x time (years) Duration of the Bond is year Duration of Bond Y Year Cash flow 0% Proportion of bond value Proportion of bond value x time (years) Duration of the Bond is.6 years Let x be the investment in Bond X and therefore investment in Bond Y shall be ( - x). Since the required duration is year the proportion of investment in each of these two securities shall be computed as follows: = x + ( - x ).6 x = 0.6 Accordingly, the proportion of investment shall be 6% in Bond X and 9% in Bond Y respectively. Amount of investment Bond X Bond Y PV of `,00,000 for 0% x 6% PV of `,00,000 for 0% x 9% = `,00,000 (0.86) x 6% = `,00,000 (0.86) x 9% = ` 0,86 = `, No. of Bonds to be purchased No. of Bonds to be purchased = ` 0,86/` 9. =.9 i.e. approx. = `,/` 96. =.0 i.e. approx. bonds bonds Note: The investor has to keep the money invested for two years. Therefore, the investor can invest in both the bonds with the assumption that Bond X will be reinvested for another one year on same returns. 9

10 . The only way the holder of an 8% bond can find a buyer is to sell the bond at a discount, so that its yield to maturity is the same as the coupon rate on new issues. Let s say interest rates increase from 8% to 0%. With years to maturity, an 8% bond has to be priced so that the discount, when amortized over years has a yield to maturity of 0%. That discount is a little under ` 00: Coupon Rate Prorated Discount ` 80 ` 00 / yrs ` 9. YTM 0.% Face Value Purchase Pr ice / `, 000 ` 800 / ` 900 The 8% bond with years to maturity must sell at a little over ` 800 to compete with 0% bonds. The possibility that interest rates will cause outstanding bond issues to lose value is called Interest rate risk. Yet there is an upside to this risk. If interest rates decline during the five years that the 8% bond is outstanding, the holder could sell it for enough of a premium to make its YTM rate equal to the lower yields of recent issues. For instance, should Interest rates decline to %, the price of the 8% bond with years to maturity will increase by about ` (i) Current Market Price of Bond Time CF PVIF 8% PV (CF) PV (CF) PV CF i. e. P Say `.00 (ii) Minimum Market Price of Equity Shares at which Bondholder should exercise conversion option:.00 Rs (iii) Duration of the Bond Year Cash flow 8% Proportion of bond value Proportion of bond value x time (years)

Bond Analysis & Valuation Solutions

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