Answer:
YTM = 10.5%
Explanation:
Solution
Given that:
The cash flow related with the 5% bond are computed below:
t = 0 1 (50) 2 (50) 3(50) 4 (50) 5(1050)
Now,
We calculate the discount factors which is given below:
1 /1 + r₁ = 920/1000 = 0.92
1/(1 + r₂)² = 860/1000 = 0.86
1/(1 + r₃)³ = 790/1000 = 0.79
1/(1 + r₄)⁴ = 700/1000 = 0.7
1/(1 + r₅)⁵ = 600/1000 0.6
Thus,
P₅% bond = 50 (0.92) + 50 (0.86) + 50 (0.79) + 50 (0.7) +1050 (0.6)
=$793. 50
For the yield to maturity (YTM) is refereed to as the IRR of this bond.
Now to solve for the YTM we have teh following.
P₅% bond = 50/YTM ║ 1- 1/(1 +YTM)⁵║ + 1000/(1+ YTM)⁵
793.5 = 50/YTM ║ 1- 1/(1 +YTM)⁵║ + 1000/(1+ YTM)⁵
Therefore
YTM = 10.5%
Note: the present value of all coupons was computed by applying the annuity formula, also added the PV of the face value
