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Vulcan, Inc., has 7 percent coupon bonds on the market that have 13 years left to maturity. The bonds make annual payments and have a par value of $1,000. If the YTM on these bonds is 8.4 percent, what is the current bond price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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Answer:

Current bond price  is $891.74

Explanation:

Coupon rate: 7%

Tenor (Nper): 13 years

Par value: $1,000

YTM (discounting rate): 8.4%

Coupon received annually (PMT) = $1,000 * 7% = $70

Current bond price  = present value of coupon received annually + present value of bond

To calculate PV of coupon received, we use excel in formula PV(discounting rate ,Nper,- PMT) = PV(8.4%,13,-70) = $541.30

or calculate manually = 70/(1+8.4%)^13+70/(1+8.4%)^12+…..+70/(1+8.4%)^1 =  $541.30

present value of bond = 1000/(1+8.4%)^13 = $350.44

Current bond price   = $541.30 + $350.44 = $891.74

The bond in which the face price is repaid at the time of maturity is called a zero-coupon bond. Coupon bonds are values paid as annual interest.

The current bond price is $891.74.

The bond price can be explained as:

Given,

  • Coupon rate = 7%

  • Years left for maturity (Nper) = 13 years

  • Par value = $1,000

  • YTM (discounting rate) = 8.4%

Coupon received annually (PMT):

[tex]= \$1,000 \times 7\% \\\\= \$70[/tex]

[tex]\rm Existing \; bond \; value = Present\; value \;of \;coupon\; received\; annually\; +\; Present \;value \;of \;the \;bond.[/tex]

To calculate PV of coupon received:

[tex]\rm PV(discounting\: rate ,Nper,- PMT) = PV(8.4\%,13,-70) \\\\= \$541.30[/tex]

[tex]\rm Present value \:of\: bond = \dfrac{1000}{(1+8.4\%)^{13}} \\\\= \$350.44[/tex]

[tex]\rm Current\; bond\; price (CP) = \$541.30 + \$350.44[/tex]

CP = $891.74

Thus, the current bond value will be $891.74.

To learn more about coupon bonds follow the link:

https://brainly.com/question/4357986

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