HBS Case Fixed Income Valuation
UGBA 103
Fixed Income Valuation
1A)
YTM is 4.75% at time of issuance.
YTM is 4.88% at 99 per 100.
YTM is 4.62% at 101 per 100.
1B) NTT should have been selling at $915.861M
PVpredrop = (47.5/.0475)*(1-(1/((1.0475)^2))) = 88.636M
PVpostdrop = ((30/.03)*(1-(1/((1.03)^2))))/(1.03^2) = 198.502M
PVfacevalue = 1B/(1.0475)^10 = 628.723M
PVpredrop + PVpostdrop + PVfacevalue = 915.861M
2A)
Bond A should sell at $1040.55 each.
Bond B should sell at $1000 each.
Bond C should sell at $456.38 each.
Bond A = (45/.04)*(1-(1/((1.04)^10))) + 1000/(1.04)^10 = 1040.55
Bond B = (40/.04)*(1-(1/((1.04)^20))) + 1000/(1.04)^20 = 1000
Bond C = 1000/(1.0816)^10 = 456.38
2B)
Ms. Alumm should invest in the Patriot’s bond because although it advertises a 8% YTM, they did not take into account the semiannual compounding which brings the true YTM of Patriot’s to be 8.16%. Thus the Patriot’s bond has a greater YTM than the Nationaliste’s 8.15% YTM.
3A)
She can afford a $228,213.64 mortgage.
$271,786.36 will be paid in total interest.
$20,538.90 of interest will be paid in the first year.
$4,461.10 of the principal will be paid in the first year.
$2,064.22 of interest will be paid in the final year.
$22,935.78 of principal will be paid in the final year.
Mortgage = (25,000/.09)*(1-(1/((1.09)^20))) = 228,213.64
Total Interest = (20*25,000) – Mortgage = 271,786.36
Interestfirst = Mortgage * (.09) = 20,538.90
Principalfirst = 25,000 – Interestfirst = 4,461.10
Interestfinal = (25,000/1.09) – 25,000 = 2,064.22
Principalfinal = 25,000 – Interestfinal = 22,935.78
3B)
She can afford a $273,301.84 mortgage.
PV0 = (25,000/.09)*(1-(1/((1.09)^5))) = 97,241.28
PV5 = ((30,000/.09)*(1-(1/((1.09)^5))))/(1.09^5) = 75,840.19
PV10 = ((35,000/.09)*(1-(1/((1.09)^5))))/(1.09^10) = 57,506.076
PV15 =((40,000/.09)*(1-(1/((1.09)^5))))/(1.09^15) = 42,714.29
PV0 + PV5 + PV10 + PV15 = 273,301.836
Fixed Income Valuation
1A)
YTM is 4.75% at time of issuance.
YTM is 4.88% at 99 per 100.
YTM is 4.62% at 101 per 100.
1B) NTT should have been selling at $915.861M
PVpredrop = (47.5/.0475)*(1-(1/((1.0475)^2))) = 88.636M
PVpostdrop = ((30/.03)*(1-(1/((1.03)^2))))/(1.03^2) = 198.502M
PVfacevalue = 1B/(1.0475)^10 = 628.723M
PVpredrop + PVpostdrop + PVfacevalue = 915.861M
2A)
Bond A should sell at $1040.55 each.
Bond B should sell at $1000 each.
Bond C should sell at $456.38 each.
Bond A = (45/.04)*(1-(1/((1.04)^10))) + 1000/(1.04)^10 = 1040.55
Bond B = (40/.04)*(1-(1/((1.04)^20))) + 1000/(1.04)^20 = 1000
Bond C = 1000/(1.0816)^10 = 456.38
2B)
Ms. Alumm should invest in the Patriot’s bond because although it advertises a 8% YTM, they did not take into account the semiannual compounding which brings the true YTM of Patriot’s to be 8.16%. Thus the Patriot’s bond has a greater YTM than the Nationaliste’s 8.15% YTM.
3A)
She can afford a $228,213.64 mortgage.
$271,786.36 will be paid in total interest.
$20,538.90 of interest will be paid in the first year.
$4,461.10 of the principal will be paid in the first year.
$2,064.22 of interest will be paid in the final year.
$22,935.78 of principal will be paid in the final year.
Mortgage = (25,000/.09)*(1-(1/((1.09)^20))) = 228,213.64
Total Interest = (20*25,000) – Mortgage = 271,786.36
Interestfirst = Mortgage * (.09) = 20,538.90
Principalfirst = 25,000 – Interestfirst = 4,461.10
Interestfinal = (25,000/1.09) – 25,000 = 2,064.22
Principalfinal = 25,000 – Interestfinal = 22,935.78
3B)
She can afford a $273,301.84 mortgage.
PV0 = (25,000/.09)*(1-(1/((1.09)^5))) = 97,241.28
PV5 = ((30,000/.09)*(1-(1/((1.09)^5))))/(1.09^5) = 75,840.19
PV10 = ((35,000/.09)*(1-(1/((1.09)^5))))/(1.09^10) = 57,506.076
PV15 =((40,000/.09)*(1-(1/((1.09)^5))))/(1.09^15) = 42,714.29
PV0 + PV5 + PV10 + PV15 = 273,301.836