Duck, an accrual basis corporation, sponsored a rock concert on December $29,2022.$ Gross receipts were $$300,000.$ The following expenses were incurred and paid as indicated:

Expense$$Payment DateRental of coliseum$$25,000$December $21,2022$Cost of goods sold:$$Food$30,000$December $30,2022$Souvenirs$60,000$December $30,2022$Performers$100,000$January $5,2023$Cleaning the coliseum$$10,000$February $1,2023$

Because the coliseum was not scheduled to be used again until January $15,$ the company with which Duck had contracted did not perform the cleanup until January $810,2023.$

b$.$What is the true cost to Duck if it had to defer the $$100,000$ deduction for the performers until $2023?$ Assume a $5\%$ discount rate and a $21\%$ marginal tax rate in $2022$ and $2023.$ The present value factor for a single sum at $5\%$ for one year is $0\mathrm{.}9524.$