Question

Historic Artifacts, Inc. has the following two bonds outstanding.  Use the information to get the weighted average cost of debt for Historic Artifacts.

Bond A                        Bond B

Face Value                                         1000                                         1000

Current price                                       105                                          98

Coupon rate                                       6%                                            5%

Years to maturity                                 13                                            8

Number of bonds outstanding            7,500                                        6,000

Compounding                                    Annual                        Semiannual

YTM on Bond A _____________

YTM on Bond B _____________

Market Value % on Bond A ______________

Market Value % on Bond B ______________

Weighted Average Cost of Debt __________

Answer 1

Calculation of YTM of Bond A :

Using Financial Calculator

=RATE(nper,pmt,pv,fv)

where nper is Number of years i.e 13

pmt is Interest payment i.e 1000 * 6% =60

pv is Current Market Price

= - 1050 (1000 * 105%)

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(13,60,-1050,1000)

therefore ,Yield to maturity is 5.422356%

Calculation of YTM of Bond B :

Using Financial Calculator

=RATE(nper,pmt,pv,fv)

where nper is Number of years i.e 8 * 2 = 16 (As semi annual Coupon Payment)

pmt is Interest payment i.e 1000 * 5% =50/2 = 25 (As semi annual Coupon Payment)

pv is Current Market Price

= - 980 (1000 * 98%)

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(16,25,-980,1000)

therefore ,Yield to maturity is 2.655053% (Semiannual)

Yield to maturity is 2.655053%* 2 =5.310105% (Annual)

Market Value on Bond A = Number of Bonds outstanding * Current price

= 7500 * 1050

= 7,875,000

Market Value on Bond B = Number of Bonds outstanding * Current price

= 6000 * 980

= 5,880,000

Total Market Value = Market Value on Bond A + Market Value on Bond B

= 7,875,000 + 5,880,000

=13,755,000

Market Value % on Bond A = Market Value on Bond A / Total Market Value

= 7,875,000 / 13,755,000

= 0.5725

Market Value % on Bond B = Market Value on Bond B / Total Market Value

=5,880,000 / 13,755,000

= 0.4275

Weighted Average Cost of Debt = (YTM on Bond A * Market Value % on Bond A) + (YTM on Bond B * Market Value % on Bond B)

= (5.422356% * 0.5725) + (5.310105% * 0.4275)

= 3.10429881 + 2.27007

= 5.3744% or 5.37%