Question

Peter and Mark are considering buying a Treasury Bill that promises to pay $100 000 in 91 days. Peter has a time value of money of 8% per annum and Mark has a time value of money of 6% per annum. 

a) Identify, with reason(s) which one of the two will be willing to pay more for the Treasury Bill.

b) Suppose the Treasury Bill was for 182 days, what would this change in maturity do to the price that either Peter or Mark would be wiling to pay

Answer 1

a) Since Time value of money is higher for Peter compared to Mark i.e. 8% compared to 6% p.a therefore Mark would be willing to pay more for the treasury bill since 100000 discounted at 6% would result in more amount payable compared to 100000 discounted at 8%. This can be proved as per the below calculation:

Interest rate for 91 days = Peter - 8/365 * 91 = 2% , Mark - 6/365 * 91 = 1.5%

Amount of money willing to be paid

Peter - 100000*1/1.02 = $98039.21569 i.e. $98039.22

Mark - 100000*1/1.015 = $98522.16749 i.e. $98522.17

b) If the treasury bill was for 182 days instead of 91 days this change would reduce the price that either Peter or Mark are willing to pay since the discounting rate would be now higher as can be seen from below calcualtion:

Interest rate for 182 days = Peter - 8/365 * 182 = 4% , Mark - 6/365 * 182 = 3%

Amount of money willing to be paid

Peter - 100000*1/1.04 = $96153.8462 i.e. $96153.85

Mark - 100000*1/1.03 = $97087.3786 i.e. $97087.38

Reduction in price willing to pay if maturity increases to 182 days

Peter - $98039.22 - $96153.85 = $1885.37

Mark - $98522.17 - $97087.38 = $1434.79