Please help with the following questions. 1) You are analyzing a 4.6% coupon bon
ID: 2798481 • Letter: P
Question
Please help with the following questions. 1) You are analyzing a 4.6% coupon bond that pays interest annually. It has a par value of $1,000 and is now selling for $1,065. It matures in eight years. Face value $1,000. Calculate: a) Current Yield b) Yield to maturity 2) Find the duration of a 5% coupon bond making annual payments with three years to maturity and a yield to maturity of 4.55%. Face Value $1,000. 3) You are analyzing a 5% coupon bond making annual payments and with three years until maturity. The yield to maturity if 4.55%, what is the modified duration? Face Value $1,000. 4) What is the duration of a zero coupon bond that matures in 15 years and is currently selling for $32. 5) You are considering investing in a no load mutual fund that has had excellent performance. At yesterday's closing price the total assets of this mutual fund were $920 Million and it liabilities were $8 Million. The fund has 17.9 Million shares outstanding. What is its NAV as of yesterday's close.Explanation / Answer
Requirement 1(a):
Current Yield = Interest / Market Price
= 1000*4.6% / 1065
= 46 / 1065
= 4.3192%
= 4.32%
Requirement 1(b):
Market Price = Present Value of cash flows = PV of Interest + PV of maturity value
Market Price = [Interest * PVAF(YTM, 8)] + [Maturity Value * PVIF(YTM, 8)]
$1065 = [$46 * PVAF(YTM, 8)] + [$1000 * PVIF(YTM, 8)]
If YTM = 4%, Market Price = $1040.396469
If YTM = 3%, Market Price = $1112.315
For 1% decrease in YTM, Market Price increases by $71.918531 (1112.315-1040.396469)
For how much decrease in YTM, Market Price increases by $24.603531 (1065-1040.396469)?
Answer is 0.3421(24.603531/71.918531)
YTM = 4 - 0.3421 = 3.6579% = 3.66%
Requirement 2:
Duration of bond = 2895.685 / 1012.358685 = 2.86 years
Requirement 3:
Modified Duration = Duration / (1+YTM/n)
= 2.86 / (1+0.0455)
= 2.86 / 1.0455
= 2.73%
Requirement 4:
Duration of Zero Coupon Bond = Life of the Zero Coupon Bond = 15 years
Requirement 5:
NAV = Net Assets / Outstanding Shares
= (Assets - Liabilties) / Outstanding shares
= ($920 million - $$8 million) / 17.9 million
= $912 million / 17.9 million
= $50.9497
= $50.95
Calculation of Duration of bond: Year (x) Cash flow PVF (4.55%) PV of CF (W) Wx 1 50 0.956480153 47.82400765 47.82401 2 50 0.914854283 45.74271416 91.48543 3 1050 0.875039965 918.791963 2756.376 1012.358685 2895.685