Final answer:
After a 0.5% decrease in market interest rates, the market value of the $200 million bond portfolio with a 6% coupon rate will increase, and the market value of the $150 million 3-year note with a 5% coupon rate will decrease. This is because the present value of future cash flows is higher at lower discount rates for assets and lower for liabilities.
Step-by-step explanation:
To determine the true market value of the bond portfolio and the note after a decrease in market interest rates, we must calculate the present value of future cash flows using the new market rates. Since all market rates have decreased by 0.5%, we would use these new rates to discount the future cash flows from both the bonds and the note.
For the $200 million bonds with a fixed annual coupon rate of 6%, the true market value will increase because the present value of future cash flows is higher when discounted at the new lower rates. Similarly, for the $150 million 3-year note at an annual coupon rate of 5%, the liability of the bank will decrease, as the present value of what they need to pay back is now lower at the new reduced interest rates.
The exact calculation would require knowing the payment schedule of the bonds and the note (whether they pay annually or semi-annually, for example) and then using the present value formula for each cash flow. However, the general effect of a decrease in interest rates is an increase in the value of existing bonds and a decrease in the value of existing liabilities such as notes or loans with fixed interest rates.
As a comparison and example, think of a two-year bond issued for $3,000 with an 8% interest rate, which pays $240 in interest annually. If the discount rate (interest rates) decreases from 8% to 7.5%, the present value of the bond's future cash flows would increase, indicating a rise in the bond's market value.