Bond Valuation, Interest and YTM Problem

zowmaster

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Mar 3, 2015
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3
Having a little trouble figuring out where the 1,000.84 comes from in the 10% yield column from the question below, I'm good with the interest and yield sections. I know its probably the present value of the coupon payments for years 7-10 (see attachment) or possibly the discounted future value? The latter actually comes closer to me in terms of getting the 1,000.84, but logically I feel like it should be the present value of the coupons from years 7-10... Any thoughts on where I'm going wrong? Thanks and much appreciated :)

Problem:

Assume receipt of 75.9% of the coupon in last year, since the bond will be held for 75.9% of that year.


Assume reinvestment of coupon at 10% for first three years , then reinvestment at the prevailing market yield after

12% indicates 10% for the first three years and 12% after that.
10% indicates 10% for the entire time period.
8% indicates 10% for the first three years and 8% after that.

Beginning of holding period: January 1st
YTM = 10% on January 1st; There is a flat yield curve.
End of holding period is October 4, after 6.759 years.
Length of holding period is 6.759 years.
Duration = 6.759 years

Strategy Three: Buy a 10% Bond with a 10 year maturity as of January 1st
Sell the bond on October 4th after 6.759 years.

Market Yields Bond value on Interest on Coupons Yield
and Beyond October 4th

12% ? ? ?

10% 1000.84 229.44 10.01

8% ? ? ?
 
Grr, having trouble posting my .xls spreadsheet so I'll try to copy and paste my work here, sorry in advance for the mess..


CFSFVs
11001.731332173.13324691
21001.573939157.39386082
31001.430853143.0853283
41001.300776130.0775709PVCOUPONINTFVPV4
51001.182523118.25233721000675.9229.4444691905.34$1,000.005
61001.075021107.50212476
6.75975.9175.9905.3444697
675.9905.3444687229.44451000.848
724.10.9121.909316.7591906.1844699
81000.8382.6410
91000.7575.13FV =PV(1+k)^1/n
1011000.68751.31000
3.2411324.11000.841.90618447
YIELD1.1001468210.01%
-1
0.10014682
100
10.0146819
CFSFVs
11001.731332173.1332469
21001.573939157.3938608
31001.430853143.085328
41201.300776156.0930851
51201.182523141.9028047
61201.075021129.0025497PVCOUPONINTFV
6.75991.08191.081000751.08240.611991.6910.73%1.99169091.107312
751.08991.6908753240.6109
925.56
CFSFVs
11001.731332173.1332469
21001.573939157.3938608
31001.430853143.085328
4801.300776104.0620568
5801.18252394.60186978
6801.07502186.0016998PVCOUPONINTFV
6.75960.72160.721000600.72218.2780621819.009.26%1.81899811.092553
600.72818.9980621218.2781
 
For those interested I found the solution; the 1,000.84, or present value of the bond on year 6 October 4th, is derived from the PV of the payments from years 7-10 (duh). Where I was going wrong was I was using a wrong N (time)factor. Instead of starting with N-6.759 (N = year 7), I used 0 as the first value...

Here is the update for those that care;

724.1($23.55)
8100($88.84)
9100($80.77)
101100($807.68)
3.2411324.1$1,000.84
Value of 10% Bond on October 4th Year 6




 
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