Question

The time from acceptance to maturity on a $50,000 banker's acceptance is 180 days. The importing bank's acceptance commission is 2.50 percent and the market rate for 180-day B/As is 2 percent.

If the exporter's opportunity cost of capital is 11 percent, should he discount the B/A or hold it to maturity?

Answer 1

ANSWER TO THIS QUESTION

The time from acceptance to maturity on a $50,000 banker's acceptance is 180 days.
The importing bank's acceptance commission is 2.50 percent and that the market rate for 180-day B/As is 2 percent.

The amount the exporter will receive if he holds the B/A until maturity.

= $50,000*(1- (0.025*180/360))

= $49,375

The amount the exporter will receive if he discounts the B/A with the importer's bank.

=$50,000*(1-(0.02+0.025)*180/360)

=$48,875

The bond equivalent yield the importer's bank will earn from discounting the B/A with the exporter.

If the exporter holds the B/A to maturity he will receive:
= $50,000*(1- (0.025*180/360))

= $49,375

If the exporter discounts the B/A with the importer bank he will receive:
=$50,000*(1-(0.02+0.025)*180/360)

=$48,875

The bond equivalent yield that the exporter pays in discounting the B/A is
={{$48,875/$49,375}-1}*365/180

= -0.0205

.

If the exporter's opportunity cost of capital is 11 percent, should he discount the B/A or hold it to maturity?

If his cost of funds > 2.05% compounded semiannually (EAR = 2.06%), he should discount the B/A.
The exporter pays the acceptance commission regardless of whether he discounts the B/A or holds it to maturity, hence it is not marginal to a decision to discount the B/A.
You could also make this determination based on this calculation:

= $48,875*(1+0.11*180/360)

=  $ 51,563.13>$49,375