Cost of irredeemable debt

Hi there, I hope you’re well?

Looking at the chapter on the Cost of Capital I’ve attempted a question in the Kaplan Integrated workbook but my answer is not consistent with the answer at the end of the chapter – please could I have your help with this?

The question is:

A company has irredeemable loan notes in issue trading at $95 cum interest.
The coupon rate is 5% and the rate of corporation tax is 30%.
Calculate the pre-tax and post-tax cost of debt.

My answer is:

Pre-tax cost of debt (aka return required by the investor):

I = 5% * $95 = $4.75
MV = $95 – $4.75 = $90.25
Pre-tax cost of debt (return required by the investor) = $4.75 / $90.25

Post-tax cost of debt (aka the cost of debt to the investee):

I * (1 – T) = 5% * $95 * 0.7 = $3.33
MV = $95 – $4.75 = $90.25
Post-tax cost of debt (cost of debt to the investee): $3.33 / $90.25 = 3.68%

Answer per Kaplan:

Ex interest MV = $95 – ($100 × 5%) = $90
Kd = I/MV
Kd = $5/$90 = 0.056 or 5.6%

Kd(1 – T) = I (1 – T)/MV
Kd(1 – T) = ($5 × 0.7)/$90 = 0.039 or 3.9%

I’ve naively assumed here that the cum interest market value is the nominal value of the loan note in the absence of all other information (using this to calculate my I value) and so can’t quite fathom the conclusion that the nominal value of the instrument is $100, hence calculating I as $5, rather than my $4.75.

I appreciate that in practice you cannot use the cum-interest value of a loan note as it’s nominal value for the basis of subtracting interest from to get the ex-interest value (since the coupon rate * nominal value would give the interest), but is there any information given in this question which would actually allow me to calculate the nominal value of $100?

Thanks.