The following questions relate to Kyle Company, which manufactures products KA$,$ KB$,$ and KC from a joint process. Joint product costs were $$189,000.$ Additional information follows.

If Processed Further

Product Units Produced Sales Value at Split$-$Off Sales Values Additional Costs

KA $84,000$ $ $240,000$ $ $330,000$ $ $54,000$

KB $60,000210,000270,00042,000$

KC $24,000150,000240,00030,000$

Required:

a$.$ Assuming that joint product costs are allocated using the physical quantities $($units produced$)$ method, what was the total cost of product KA $($including $$54,000$ if processed further$)?$

b$.$ Assuming that joint product costs are allocated using the sales value at split$-$off $($net realizable value method$),$ what was the total cost of product KB $($including the $$42,000$ if processed further$)?$

This is what I have so far :

a$.$ Physical Quantities Method for product KA: First, we need to calculate the total units produced:

Total Units $=84,000($KA$)+60,000($KB$)+24,000($KC$)=168,000$ units

Next, we allocate the joint product costs based on the proportion of units produced. For product KA$,$ this is:

Joint Cost Allocation $($KA$)=$ Total Joint Product Costs $*($Units Produced by KA $/$ Total Units$)=$ $$189,000*(84,000/168,000)=$ $$94,500$

Finally, we add the additional processing cost for product KA to get the total cost:

Total Cost $($KA$)=$ Joint Cost Allocation $($KA$)+$ Additional Processing Cost $($KA$)=$ $$94,500+$ $$54,000=$ $$148,500$

b$.$ Sales Value at Split$-$Off Method for product KB: First, we need to calculate the total sales value at split$-$off:

Total Sales Value at Split$-$Off $=$ $$240,000($KA$)+$ $$210,000($KB$)+$ $$150,000($KC$)=$ $$600,000$

Next, we allocate the joint product costs based on the proportion of sales value at split$-$off. For product KB$,$ this is:

Joint Cost Allocation $($KB$)=$ Total Joint Product Costs $*($Sales Value at Split$-$Off for KB $/$ Total Sales Value at Split$-$Off$)=$ $$189,000*($$$210,000/$ $$600,000)=$ $$66,300$

Finally, we add the additional processing cost for product KB to get the total cost:

Total Cost $($KB$)=$ Joint Cost Allocation $($KB$)+$ Additional Processing Cost $($KB$)=$ $$66,300+$ $$42,000=$ $$108,300$

So$,$ the total cost of product KA $($including $$54,000$ if processed further$)$ using the physical quantities method is $$148,500,$ and the total cost of product KB $($including the $$42,000$ if processed further$)$ using the sales value at split$-$off method is $$108,300.$