Answer:
-5.14 for sam
-18.01% for dave
Explanation:
We first calculate for Sam
R = 7.3%
We have 2% increase
= 9.3%
We calculate for present value of coupon and present value at maturity using the formula for present value in the attachment
To get C
1000 x 0.073/2
= 36.5
time= 3 years x 2 times payment = 6
Ytm = rate = 9.3%/2 = 0.0465
Putting values into the formula
36.5[1-(1+0.0465)^-6/0.0465]
= 36.5(1-0.7613/0.0465)
36.5(0.2385/0.0465)
= 36.5 x 5.129
Present value of coupon = 187.20
We solve for maturity
M = 1000
T = 6 months
R = 0.0465
1000/(1+0.0465)⁶
= 1000/1.3135
Present value = 761.32
We add up the value of present value at maturity and that at coupon
761.32 + 187.20
= $948.52
Change in % = 948.52/1000 - 1
= -0.05148
= -5.14 for sam
We calculate for Dave
He has 20 years and payment is two times yearly
= 20x2 = 40
36.5 [1-(1+0.0465)^-40/0.0465]
Present value = 36.5 x 18.014
= 657.511
At maturity,
Present value = 1000/(1+0.0465)⁴⁰
= 1000/6.1598
= 162.34
We add up these present values
= 657.511+162.34 = $819.851
Change = 819.851/1000 -1
= -0.1801
= -18.01%
