Question

20. The Company has a $48,000 pure discount bond that comes due in one year. The risk-free rate of return is 3 percent. The firm's assets are expected to be worth either $45,000 or $55,000 in one year. Currently, these assets are worth $50,000. What is the current value of the firm's debt?

		$43,724.75
		$47,681.49
		$46,277.13
		$45,582.52
		$44,106.59

Answer 1

Answer: Option(4) $45,582.52

If the Value of assets after 1 year is above $48,000, The deep discount bond will be copletely paid off. However if the value of assets is not sufficient to pay the liabilities, the libility will be honoured only to the extent of value of assets.

That is if the value of asets after 1 year is above $48,000, the bonds will be redeemed for $48,000.

However the value of assts falls to $45,000 after 1 year, the bond hilders will be paid only $45,000.

Current Value of Assets (So) = $ 50,000

Risk free Rate (r) = 3%

Expected Price in a 1 Year

S(upward) = $55,000

S(downward) = $45,000

Risk Neutralisation Model:

Fair Future Price = So * (1+i)^n

Fair Future Price = $50,000* (1+0.03)^1

Fair Future Price = $50,000* 1.03

Fair Future Price = $ 51,500

Let the Probability of attaining Upward price after 1 year = "P"

Then,

($55,000 * P) + ($45,000 * (1 - P)) = $ 51,500

($55,000 - $45,000) P = $51,500 - $45,000

$10,000 P = $6,500

P(Upward) = 0.65

Therefore P(Downward) = 1- 0.65

P(Downward) = 0.35

Therefore, Price of Pure DiscountBond after 1 Year =

= [(0.65 * $48,000) + (0.35 * $45,000]

= $46,950

Therefore, Price of Pure DiscountBond Today = Expected Price after 1 year * PV(3%,1 Year)

Price of Pure DiscountBond Today = $46,950 / (1+0.03)

Price of Pure DiscountBond Today = $45,582.5