OPS 461
What must be the price of a $1000 bond with a 5.8% coupon rate, annual coupons, and 20 years to maturity if YTM is 7.8% APR? A)$960.82 B) 1120.95 C) $800.68 D) $640.54
C) $800.68 FV = $1000, n = 20, PMT = 58, I = 7.8% per period, calculate PV = $800.68
How are investors in zero-coupon bonds compensated for making such an investment? A. Such bonds are purchased at their face value and sold at a premium on a later date. B. Such bonds make regular interest payments. C. Such bonds are purchased at a discount, below their face value. D. Such bonds have a lower face value as compared to other bonds of similar term
.C. Such bonds are purchased at a discount, below their face value.
A bond with an annual coupon of $100 originally sold at par for $1,000. The current market interest rate on this bond is 9%. Assuming no change in risk, this bond will sell at a _____ today and present the seller with a capital _____ .a.premium; gain b.discount; gain c.premium; loss d.discount; loss e.discount; neither loss or gain
Answer: A. .a.premium; gain Note the seller will realize a capital gain. The buyer who purchases this premium bond and holds until maturity will realize a capital loss.
Which of the following is true about the face value of a bond? A. It is the notional amount we use to compute coupon payments B. It is the amount that is repaid at maturity. C. It is usually denominated in standard increments, such as $1,000. D. All of the above are true.
D. All of the above are true.
Quirke PLC has bonds outstanding with 20 years remaining maturity. Interest is paid annually at a coupon rate of 7.6%. The YTM on these bonds is 8.2%. What is the bond's current price?
Similar to above, only with annual coupons and an annual YTM, which simplifies matters. Calculator: N= 20 PMT = coupon amount = .076*1000=76 FV = 1000 I=8.2% Solve for PV = $941.96
Explain, in your own words, what the YTM is and how it is calculated.
The YTM is the single discount rate that will discount a bond's CFs to its price. It is the annual rate of return, expressed as an APR, that the investor will earn if they buy the bond at its current price and hold it until maturity—assuming the bond pays the contractual CFs as agreed. Finally, conceptually, the YTM is like a complicated weighted average of the market rates (r1, r2 , etc.) used to price a bond.
If interest rates go down, will the bond be worth more or less? Why?
The bond will be worth more. There are two ways to think about this: first, interest rates enter into the denominator of the PV calculation, so the PV goes up and PV is the price of the bond. Second, and more importantly is the economic intuition that the bond's package of cash flows hasn't changed, but it has become more attractive relative to what's being offered currently.
d. If interest rates go down, will the principal repayment be a larger or smaller portion of the total value of the bond? Why?
The principal will become a larger proportion of the bond's value. While the bond's value will go up, the principal's value will go up more than proportionately because of the compounding effect of 200 periods of lower interest rates. Effectively, the final payment is not being discounted as much relative to the other payments.
The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 8.2% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 7.3%, then the price that this bond trades for will be closest to ________. A) $1063 B) $850C) $1276D) $1488
A) $1063 N = 20 (10 × 2) ; I = 3.65 (7.3/2) ; PMT = (.082*1000)/2 = $41 ; FV = $1000 ; Compute PV = 1063.10
What must be the price of a $10,000 bond with a 6.1% coupon rate, semiannual coupons, and five years to maturity if it has a yield to maturity of 10% APR? A) $8494.26B) $10,193.11C) $11,891.97D) $6795.41
A) $8494 FV = $10,000, semiannual PMT = (.061 x 10000)/ 2 = 305 ; periodic discount rate = 10%/2 = 5%, calculate PV = $8494.26
Why do bond prices and interest rates move inversely? Give an explanation based on economic intuition.
As with any present value, we evaluate the future cash flows from the bond by comparing them to the returns offered on alternative investments in the market. Interest rates represent the returns offered on alternative investments in the market, so if interest rates increase, then the bond looks relatively less attractive as an investment. It is important to note that the bond offers a fixed deal in the sense that the cash flows from the bond are set and do not change, so the attractiveness of that particular package of cash flows is dependent on the returns offered elsewhere.
A risk-free, zero-coupon bond with a face value of $10,000 has 15 years to maturity. If the YTM is 6.1%, which of the following would be closest to the price this bond will trade at?A) $4937 B)$5760 C) $6582 D) $4114
Answer: D) $4114 Price = Face value / (1 + YTM)N. Price = ($10,000) / (1 + 6.1%)15 = $4114. Or financial calculator.
Consider a zero-coupon bond with a $1000 face value and 15 years left until maturity. If the bond is currently trading for $431, then the yield to maturity on this bond is closest to ________. A) 2.89% B) 56.90% C) 43.10% D) 5.77%
D) 5.77% N = 15 ; PV = -431; PMT = 0; FV = 1000; Compute I = 5.7714%.
A bond has five years to maturity, a $1000 face value, and a 5.5% coupon rate with annual coupons. What is its yield to maturity if it is currently trading at $846.11? A) 11.41%B) 13.31%C) 7.61%D) 9.51%
D) 9.51% FV = $1000, periods = 5, PMT = 55.00, and PV = $846.11, calculate rate = 9.5089% per period.
The yield to maturity of a $1000 bond with a 7% coupon rate, semiannual coupons, and two years to maturity is 7.6% APR, compounded semiannually. What must its price be?
Given the yield, we can compute the price. First, note that a 7.6% APR is equivalent to a semiannual rate of 3.8%. Also, recall that the cash flows of this bond are an annuity of four payments of $35, paid every six months, and one lump-sum cash flow of $1,000 (the face value), paid in two years (four six-month periods). 35/(1+.038)^1 + 35/(1+.038)^2+ 35/(1+.038)^3 1000+35(1+.038)^4 pv= 989.06 So the price must be $989.06. The yield to maturity is the discount rate that equates the present value of the bond's cash flows with its price. By discounting the cash flows using the yield, we can find the bond's price.
Which of the following statements regarding bond pricing is true? a.The lower the market interest rate, the more valuable the coupon payments are today b.When market interest rates rise, bond prices will also rise, all else the same. c.Bonds with short maturities are generally (all else the same) more sensitive to changes in interest rates than bonds with longer maturities. e.All else the same, bonds with larger coupon payments will have a lower prices today.
a.The lower the market interest rate, the more valuable the coupon payments are today.
Which bond would most likely possess the least degree of interest rate risk? a.8% coupon rate, 10 years to maturity b.10% coupon rate, 10 years to maturity c.12% coupon rate, 10 years to maturity d.8% coupon rate, 20 years to maturity e.12% coupon rate, 20 years to maturity
c.12% coupon rate, 10 years to maturity
Which of the following statements are false?I.A bond with a coupon rate below its required return (YTM) should sell at a discount. II. A downward-sloping yield curve is relatively rare, and often precedes a recession. III. In general bond prices move in the same direction as changes in the discount rate. For example, when rates increase, so do bond prices.IV. The higher the credit risk of a bond, the higher the return investors will require from that bond.a.I only b.II only c.III only d.IV only e.I & II only f.I & III only g.I, II & III only h.I & IV only j.II & III only k.I, II & IV only m. II & IV only n. III & IV only o.II, III & IV only p.I, III & IV only q.none of these
c.III only
The relationship between nominal interest rates on treasury securities and the time to maturity is called the: a.Liquidity effect. b.Fisher effect. c.Yield curve, aka term structure of interest rates. d.Inflation premium.e.Interest rate risk premium.
c.Yield curve, aka term structure of interest rates.
The yield to maturity on a semiannual payment bond is typically quoted as . a.an EAR b.a six-month rate c.an APR d. a compound rate e.a current yield
c.an APR
A bond with a face value of $1,000 has annual coupon payments of $100 and was issued 7 years ago. The bond currently sells for $1,000 and has another 5 years remaining to maturity. This bond's ____ must be 10%. I.yield to maturity II. market premium III. coupon rate a.I only b.I and II only c.III only d.I and III only e. I, II and III
d.I and III only
All else the same, interest rate risk is highest for bonds with:I.Low coupon rates. II.Variable rate coupons.III.Long maturities. a.I only b.III only c.I and II only d.I and III only e.II and III only f.I, II, and III
d.I and III only
