Prob Set 2.1 1. (2 points) Assume that the annual interest rate is 5.20%. Calcul

Question

Prob Set 2.1

1. (2 points) Assume that the annual interest rate is 5.20%. Calculate the Effective Annual Return (EAR) under the following compounding assumptions (Show all work, and express answers as a percentage, e.g. 4.85%. For e, f, and g, the answers are slightly different, so be sure to report enough decimal places to show the differences.):

a. Annual

b. Semi-annual

c. Quarterly

d. Monthly

e. Daily (360 day year)

f. Daily (365 day year)

g. Continuously compounded

2. (2 points) A Ford Co. corporate bond has a coupon rate of 4.20% and a face value of $1,000 (use this information for all parts below and show all work).

a. Calculate the bond’s annual Yield to Maturity (YTM) if it is selling for $975.20, has annual coupon payments, and 5 years to maturity.

b. Calculate the bond’s price if the current YTM on bonds similar to Ford’s bonds is 5.75%, assuming annual coupon payments, and 8 years to maturity.

c. Calculate the bond’s annual YTM if it sells for $1,075.00, has semi-annual coupon payments, and 4 years to maturity.

d. Calculate the bond’s price if the current YTM on similar bonds is 6.25%, assuming semi-annual coupon paymentsand 6 years to maturity.

Explanation / Answer

Effective annual interest rate = (1+r/n)n-1 and annual interest rate r = 5.20%

Effective Interest Rate In case of Yearly payments = 5.20%

Effective Interest Rate In case of semi anually payments = (1+0.052/2)2-1 = 5.267%

Effective Interest Rate In case of Quaterly payments = (1+0.052/4)4-1 = 5.302%

Effective Interest Rate In case of monthly payments = (1+0.052/12)12-1 = 5.325%

Effective Interest Rate In case of Daily payments (360 days) = (1+0.052/360)360-1 = 5.347%

Effective Interest Rate In case of Daily payments (365 days) = (1+0.052/365)365-1 = 5.349%

Answwer 2

YTM = (C + (F - P) / n) / ((F + P) / 2)

Where

YTM = Yield to Maturity
C = Coupon or Interest Payment
F = Face Value
P = Price
n = Years to Maturity

(a) YTM = (C+(F-P)/n) / ((F+P)/2) =(42+(1000-975.20)/5) / ((1000+975.20)/2) = 4.75%

(b) YTM = (C+(F-P)/n) / ((F+P)/2) = 5.75% = (42+(1000-Bo)/8) / ((1000+Bo)/2) = Bo = 757.53

(c) YTM = (C+(F-P)/n) / ((F+P)/2) =(21+(1000-1075)/8) / ((1000+1075)/2) = 2.24% yearly

b) YTM = (C+(F-P)/n) / ((F+P)/2) = 3.125% = (42+(1000-Bo)/8) / ((1000+Bo)/2) = Bo = 1275.88

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.