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SOVA2 [1]
3 years ago
13

Below is a list of prices for zero-coupon bonds of various maturities. Maturity (Years) Price of $1,000 Par Bond (Zero-Coupon) 1

$ 949.20 2 866.42 3 817.77 a. An 8.6% coupon $1,000 par bond pays an annual coupon and will mature in 3 years. What should the yield to maturity on the bond be? (Round your answer to 2 decimal places.) b. If at the end of the first year the yield curve flattens out at 7.9%, what will be the 1-year holding-period return on the coupon bond? (Round your answer to 2 decimal places.)
Business
1 answer:
REY [17]3 years ago
7 0

Answer:

a. 6.91%

b. 8.46%

Explanation:

to calculate YTM of zero coupon bonds:

YTM = [(face value / market value)¹/ⁿ] - 1

  • YTM₁ =  [(1,000 / 949.20)¹/¹] - 1 = 5.35%
  • YTM₂ =  [(1,000 / 886.42)¹/²] - 1 = 6.21%
  • YTM₃ =  [(1,000 / 817.77)¹/³] - 1 = 6.94%

a. A 8.6% coupon $1,000 par bond pays an annual coupon and will mature in 3 years. What should the yield to maturity on the bond be?

the bond's current market price:

  • $1,000 / 1.0694³ = $817.67
  • $86/1.0535 + 86/1.0621² + 86/1.0694³ = $81.63 + $76.24 + $70.32 = $228.19
  • current market price = $1,045.86

YTM = [C + (FV - PV)/n] / [(FV + PV)/2] = [86 + (1,000 - 1,045.86)/3] / [(1,000 + 1,045.86)/2] = 70.71 / 1,022.93 = 6.91%

b. If at the end of the first year the yield curve flattens out at 7.9%, what will be the 1-year holding-period return on the coupon bond?

the bond's current market price:

$1,000 / 1.079³ = $796.04

$86/1.0535 + 86/1.079² + 86/1.079³ = $81.63 + $73.87 + $64.46 = $219.96

current market price = $1,016

you invest $1,016 in purchasing the bond and you receive a coupon of $86, holding period return = $86 / $1,016 = 8.46%

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1.If Enviromax wants to maximize profit, what price would they charge?
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Answer:

The question is incomplete. However, kindly find below the complete version of the question:

Question

Jack and Diane own Enviromax, a monopolistically competitive firm that recycles paper products. (1.)If Enviromax wants to maximize profit, what price would they charge?  (2).What is their profit per unit if they are operating at the profit maximizing output?

Answer / Explanation

(1) First before we continue to answer this question, let us define what a monopoly is: This is a kind of market situation where the sole production or manufacturing of a product have been given to a single entity.

The graph attached below will give us a proper understanding and illustration of the answer.

Where:  MR in the graph is defined as the additional revenue obtained when producers produce 1 more unit of good and the AR refers to the total revenue divided by the amount of output produced which is essentially  the price of one unit of good.

MC refers to the additional cost incurred by producers when they produce 1 more unit of good  and is upwards sloping due to increasing opportunity costs of production.  

Noting that since the firm is a monopolistic type, the MR curve is lower than the  AR curve because if the firm wants to sell an additional unit of output it will have to lower the  successive price.  This is unlike the case of a firm operating in a PC where it takes the price as given and hence has no  ability to set prices.  it should also be noted that profit maximizing for all firms (whether PC or non-PC) occurs at MC=MR. This is because if MC>MR  this means the additional cost of producing this unit of good > additional revenue obtained from selling  this unit of good and is hence not profit maximizing. If MC<MR, this implies that the firm should not stop  at producing this unit of good because it will be forgoing the additional net revenue (profit) should it do  so. Hence all firms will produce at the point where MC=MR.

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In the graph below, since AR > AC at the profit maximizing level, this implies that per unit revenue > per unit costs and the firm makes a supernormal profit (defined as what excess profit above what is  needed to keep firms in production which is normal profit) of the shaded area.  If the firm was operating in a perfectly competitive market however, then the profit maximizing point  would occur at AR =MC (since AR=MR in a PC market) and the firm would be producing at Qpc and Ppc

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sertanlavr [38]

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