Question

The chapter demonstrated that a firm borrowing in a foreign currency could potentially end up paying a very different effective rate of interest than what it expected. Using the same baseline values of a debt principal of SF1.6 ​million, a​ one-year period, an initial spot rate of SF1.4700​/$, a 5.385​% cost of​ debt, and a 40​% tax​ rate, what is the effective​ after-tax cost of debt for one year for a U.S.​dollar-based company if the exchange rate at the end of the period​ was:

a. SF1.4700​/$

b. SF1.4000​/$

c. SF1.3570​/$

d. SF1.6160​/$

Answer 1

Principle Loan amount = SF 1,600,000

Dollar equivalent on the date of receiving the loan = 1,600,000 / 1.47 = $ 1088435.37

Case - a ............ SF 1.4700 / $ at the end of one year

Amount payable after one year = Principal amount * ( 1 + r ) = 1600,000 * (1.05385) = SF 1,686,160

Dollar equivalent payable to clear loan with interest = SF 1686160 / 1.47 = 1,147,047.62

Interest = Amount paid - Amount received = 1,147,047.62 - 1,088,435.37 = 58,612.25

Cost of debt ( before tax ) = Interest / Loan * 100 = 58,612.25 / 1088435.37 * 100 = 5.385 %

Cost of debt (After tax ) = 5.385 * ( 1 - 0.40 ) = 3.231%

Case - b .............SF 1.4000/ $ at the end of one year.

Amount payable after one year = Principal amount * ( 1 + r ) = 1600,000 * (1.05385) = SF 1,686,160

Dollar equivalent payable to clear loan with interest = SF 1686160 / 1.40 = 1,204,400

Interest = Amount paid - Amount received = 1,204,400 - 1,088,435.37 = 115,964.63

Cost of debt ( before tax ) = Interest / Loan * 100 = 115,964.63 / 1088435.37 * 100 = 10.654 %

Cost of debt (After tax ) = 10.654 * ( 1 - 0.40 ) = 6.393 %

Case - c ......... SF 1.3570​/$ at the end of one year

Amount payable after one year = Principal amount * ( 1 + r ) = 1600,000 * (1.05385) = SF 1,686,160

Dollar equivalent payable to clear loan with interest = SF 1686160 / 1.3570 = 1,242,564.48

Interest = Amount paid - Amount received = 1,242,564.48 - 1,088,435.37 = 154129.11

Cost of debt ( before tax ) = Interest / Loan * 100 = 154129.11 / 1088435.37 * 100 = 14.161 %

Cost of debt (After tax ) = 14.161 * ( 1 - 0.40 ) = 8.496 %

Case - d ......... SF 1.6160 ​/$ at the end of one year

Amount payable after one year = Principal amount * ( 1 + r ) = 1600,000 * (1.05385) = SF 1,686,160

Dollar equivalent payable to clear loan with interest = SF 1686160 / 1.6160 = 1,043,415.84

Interest = Amount paid - Amount received = 1,043,415.84 - 1,088,435.37 = -45019.53

Cost of debt ( before tax ) = Interest / Loan * 100 = - 45019.53/ 1088435.37 * 100 = - 4.136 %

Cost of debt (After tax ) = 14.161 * ( 1 - 0.40 ) = - 2.482 %

Note : A negative cost of debt indicates that interest was infact saved out of principal due to weakening of SF against $