An open-end bond mutual fund is holding a three-year, $1 million face value 5 percent annual coupon bond selling at par.What is the impact on the total asset value of the fund of a 1 percent decrease in interest rates?
A)A decrease of $10,000.
B)An increase of $10,000.
C)A decrease of $26,730.
D)An increase of $27,751.
E)The answer depends upon the number of mutual funds shares outstanding.

Question

Quizplus · Accepted Answer

The total asset value of the fund will increase because the bond's market value will increase when interest rates decrease. To calculate the new market value, we need to discount the future cash flows at the new interest rate. Using the formula for the present value of a bond, we get:

PV = C * (1 - (1 + r)^-n) / r + FV / (1 + r)^n

where PV is the market value, C is the coupon payment, r is the interest rate, n is the number of periods, and FV is the face value of the bond.

At a 4% interest rate, the new market value of the bond is:

PV = $50,000 * (1 - (1 + 0.04)^-3) / 0.04 + $1,000,000 / (1 + 0.04)^3 = $1,027,751

So the increase in market value is $27,751, and this will increase the total asset value of the fund by the same amount.

An Open-End Bond Mutual Fund Is Holding a Three-Year, $1